How do you differentiate #f(x)=e^(x^2-3x-4) # using the chain rule? How do you differentiate #f(x)=sqrt(ln2x)# using the chain rule? How do you use the chain rule to differentiate #g(x)=3tan(4x)#? How do you find the first and second derivative of #y=e^(e^x)#? How do you differentiate #f(x)=e^(5x^2+7x-13)#? How do you differentiate # y =1/sqrtln(x^2-3x)# using the chain rule? If #f(x) =cos3x # and #g(x) = (2x-1)^2 #, what is #f'(g(x)) #? How do you differentiate # y= sin2x-cos2x# using the chain rule? CliffsNotes study guides are written by real teachers and professors, so no matter what you're studying, CliffsNotes can ease your homework headaches and help you score high on exams. How do you find the derivative of # y= sqrt(x^2 + cos x)# using the chain rule? How do you find the derivative of #ln((x+1)/(x-1))#? How do you use the chain rule to differentiate #y=1/(x^4+x)^2#? How do you differentiate #f(x)=xsin(1/x)#? Given #y=(sin(x))^(logx)# calculate #dy/dx# ? How do you differentiate #f(x)=xsinsqrtx# using the chain rule? How do you use the chain rule to differentiate #y=4(x^3+5)^(3/4)#? How do you differentiate #sqrt(sin^3(1/x) # using the chain rule? If #f(x) =-e^(x) # and #g(x) = tan^2x^2 #, what is #f'(g(x)) #? How do you differentiate # y =x sqrt((4-x^2) # using the chain rule? If #f(x)= cos 4 x # and #g(x) = 2 x #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the derivative of #y = e^cosh(2x)#? How do you differentiate # y =sin(ln(cos x)) # using the chain rule? If #f(x)= cos 4 x # and #g(x) = -3x #, how do you differentiate #f(g(x)) # using the chain rule? The answer is given by the Chain Rule. How do you differentiate #f(x)=-5 xe^(x/cos x)# using the chain rule? 2) Use the chain rule and the power rule after the following transformations. How do you differentiate # f(x)= (7e^x+x)^2 # using the chain rule.? The chain rule says that. How do you use the chain rule to differentiate #f(x) = e^(4x+9)#? How do you find the first and second derivative of #y=e^(alphax)sinbetax#? How do you differentiate #f(x) = e^(-5x^2)#? By the way, here’s one way to quickly recognize a composite function. How do you differentiate #f(x)=sec(4x^5)#? How do you differentiate #f(t)=root3(1+tant)#? How do you find the derivative of #x*sqrt(x+1)#? What is the derivative of #g(x)=sqrt(5-3x)#? How do you differentiate #f(x) = (−7 x^2 − 5)^8 (2 x^2 − 9)^9# ? It’s also one of the most important, and it’s used all the time, so make sure you don’t leave this section without a solid understanding. If #f(x)= cot2 x # and #g(x) = e^(-3x ) #, how do you differentiate #f(g(x)) # using the chain rule? Example. The chain rule is also used when you want to differentiate a function inside of another function. In this presentation, both the chain rule and implicit differentiation will What is the derivative for #f(x)=sqrt(x^2-1)#? How do you use the chain rule to differentiate #y=sec2x^4#? How do you use the chain rule to differentiate #y=(3x^3+1)(-4x^2-3)^4#? How do you differentiate # f(x)= sqrt((xe^x+4)^3 # using the chain rule.? How do you use the chain rule to differentiate #root11(-4x)#? How do you differentiate #f(x)=cot(e^(x)) # using the chain rule? How do you differentiate #((5x+1)^2)(2x-1)#? How do you find the derivative of #y=x^cosx#? The Chain Rule is an extension of the Power Rule and is used for solving the derivatives of more complicated expressions. Because it's so tough I've divided up the chain rule to a bunch of sort of sub-topics and I want to deal with a bunch of special cases of the chain rule, and this one is going to be called the general power rule. How do you differentiate #y=sqrt(2-e^x)#? What is the derivatives of #sec2x# and #tan2x#? How do you find the derivative of # y = sin(x cos x)# using the chain rule? How do you differentiate #f(x)=ln(cotx)# using the chain rule? How do you differentiate # f(x)=e^sqrt(lnsqrtx)# using the chain rule.? The following problems require the use of the chain rule. If #f(x)= 1/x # and #g(x) = 1/x #, how do you differentiate #f'(g(x)) # using the chain rule? How do you find the derivative of #sin(x cos x)#? How do you find the first and second derivative of #h(x)=sqrt(x^2+1)#? How do you find the derivative of #f(x) = 2x(sinx)cos(x)#? How do you differentiate #f(x)=e^(x^3-x^2-4) # using the chain rule? How do you differentiate #f(x)=sqrtsin(1/lnx^2)# using the chain rule? How do you differentiate #f(x)=cot(ln2x) # using the chain rule? How do you differentiate #f(x)=sqrtcos(1/(2x)^3)# using the chain rule? How do you differentiate #f(x)=3(tan4x)^(1/2) # using the chain rule? And I'll have a special version of the chain rule that I'll use for these and I'll call this rule the general exponential rule. What is the derivative of #sin^2 x + cos^2 x#? Chain Rule #=>y'=3((1+x)/(1-x))^2*((1+x)/(1-x))'#, #y'=3((1+x)/(1-x))^2*((1-x)(1)-(1+x)(-1))/(1-x)^2#, #y'=3((1+x)/(1-x))^2*((1-x)-(1+x)(-1))/(1-x)^2#, #y'=3((1+x)/(1-x))^2*((1-x)+(1+x))/(1-x)^2#, #y'=1/4(x^2+3x+5)^{1/4-1}cdot(x^2+3x+5)'#. How do you differentiate #f(x)=(sec^5 (1/x))^(1/3)# using the chain rule? How do you use the chain rule to differentiate #f(x)=37-sec^3(2x)#? How do you differentiate # f(x)=sqrt((7-2x^3)# using the chain rule.? How do you use the chain rule to differentiate #y=(2x-1)^4/(x+1)^2#? How do you differentiate # y =cos(3x+7) # using the chain rule? How do you differentiate #y=((x^2+1)/(x^2-1))^3#? One way to do that is through some trigonometric identities. How do you differentiate #f(t)=sin^2(e^(sin^2t))# using the chain rule? How do you find the derivative of #w=(1+4x^3)^-2#? #f(x)=cos(3^x)#. How do you find the derivative of #e^(x-1)#? How do you differentiate given #sin^2(x/6)#? Differentiate with respect to x #e^tanx/x^(1/2)# ? How do you find the derivative using the power chain rule of #y=(cos(x^4)+x^3))^8#? How do you differentiate #sqrt(2x+1)(x^2+1)#? How do I find the derivative of #ln(ln(2x))#? How do you find the derivative of #f(x)=ln (x^2+2)#? How do you find the derivative of #sqrt(1-x^2)#? How do you find the derivative of #e^(-5x^3+x)#? How do you use the chain rule to differentiate #y=((x^5+4)/(x^2-5))^(1/5)#? It states: The derivative will be equal to the derivative of the outside function with respect to the inside, times the derivative of the inside function. The chain rule states formally that . How do you use the chain rule to find the derivative of log x? If #f(x)= 1/x # and #g(x) = x^3 #, how do you differentiate #f'(g(x)) # using the chain rule? How do you use the chain rule to differentiate #y=sqrt(3x^2+4x)#? How do you differentiate # f(x)=sqrt(ln(1/(xe^x))# using the chain rule.? How do you differentiate # y = sin (ln(x)^2+2)# using the chain rule? How do you differentiate #f(x)=cos(sqrt((cosx^2))) # using the chain rule? How do you differentiate #f(x)=(2x-3)^3# using the chain rule? How do you differentiate # y =(2 x^2 − 9)^(-9) # using the chain rule? Example of Chain Rule. Identify the factors in the function. What is the derivative of # [pi(r)^2(h)]/3#? h(x) = g(x) / 1 + f(x), Differentiate the function? How do you differentiate # f(x)=xsqrt(3x-e^x)# using the chain rule.? Example 1 Use the Chain Rule to differentiate R(z) = √5z − 8. How do you use the chain rule to differentiate #y=3/(5x^2-4)#? How do you find #(d^2y)/(dx^2)# given #2x^2-3y^2=4#? If #f(x) =-e^(-3x-7) # and #g(x) = -2sec^2x #, what is #f'(g(x)) #? Example 60: Using the Chain Rule. Examples Using the Chain Rule of Differentiation We now present several examples of applications of the chain rule. How do you differentiate #f(x)=sece^(4x)# using the chain rule.? How do you differentiate #e^((2-x)^2) # using the chain rule? How do you differentiate #f(x)=(2x^5+3)cos(x^2)#? How do you find the derivative of #root3(x^-5)#? How do you differentiate # 3/4 * (2x^3 + 3x)^(-1/4)#? How do you differentiate #f(x) = sin(1/sqrt(arcsinx)) # using the chain rule? How do you differentiate #f(x)=csc(2x-x^3) # using the chain rule? If #f(x)= 1/x # and #g(x) = 1/x #, what is #f'(g(x)) #? How do you find the fourth derivative of #-5(e^x)#? How do you differentiate #f(x)=x(1-2x+x^2)^(3/5)# using the chain rule? How do you use the chain rule to differentiate #(sinx)^100#? f(x) = log13(xe^x), Differentiate the function? How do you differentiate #f(x)=csce^(4x)# using the chain rule.? How do you differentiate #f(x)=(x^2+4x+6)^5#? How do you find the derivative for #y= (x^2 + 2x + 5) / (x + 1)#? What is the first differential of #y = t^(3/2)(16-sqrtt)#? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the 1000th derivative of #y=xe^-x#? (1 point) Use the chain rule to find out where z = z²y + xy2. What is the derivative of #sin^-1 * (5x)#? How do you differentiate # f(x)=sqrt([(2x-5)^5]/[(x^2 +2)^2] # using the chain rule.? Example 59 ended with the recognition that each of the given functions was actually a composition of functions. What is the derivative of #y = (sin x)^(cos x)#? How do you find f'(0) given #f(x) =( (x^5+5)/(3cosx))^2#? The following video outlines the basic idea of the chain rule. When to Use Chain Rule. Active 27 days ago. Indeed, we have So we will use the product formula to get What is the derivative of #sin((pi/2) - x)#? How do you differentiate #f(x)=sin(3x+1)# using the chain rule? How do you find the derivative of #f(x)=(x^5+6x^2-1)(1-3x)^2#? How do you differentiate #f(x) = sqrt[ (3 x + 1) / (5 x^2 + 1)# using the chain rule? 3) You could multiply out everything, which takes a bunch of time, and then just use the quotient rule. How do you differentiate #f(x)=ln((x-1)/(x^2+1))#? How do you use the chain rule to differentiate #tan(ln(4x))#? How do you find the derivative of #(cos x)^2 - cos x#? How do you find the derivatives of the function #f(x) = sin(x^2)#? If #f(x) =cos3x # and #g(x) = (x+3)^2 #, what is #f'(g(x)) #? How do you differentiate #f(x)= 2x^3(x^3 - 3)^4 # using the chain rule? How do you find the derivative of #y= sin(sin(sin(x)))# ? How do you differentiate #f(x)=ln((x^3-x ^2 -3x + 1) ^(2/5))# using the chain rule? How do you differentiate #f(x) = (3x ^2 -3x + 8) ^4# using the chain rule? Let us find the derivative of . How do you find the derivative of #y=-(2x+3+4x^-1)^-1#? How do you differentiate #g(t)=1/(t^4+1)^3#? How do you calculate the derivative of the function #f(x)=cos(x^3+x^2+1)#? The chain rule can be tricky to apply correctly, especially since, with a complicated expression, one might need to use the chain rule multiple times. How do you differentiate #y=e^(ktansqrtx)#? How do you find the derivative of #sqrt((x^2-1) / (x^2+1))#? How do you find the derivative of #(x^2 + 1/x)^5#? How do you differentiate # y= sqrt( (x^2 + 4x + 1)^2+2x)# using the chain rule? What is the derivative of #f(x) = sqrt[ (3 x + 1) / (5 x^2 + 1) ]#? How do you use the chain rule to differentiate #ln(-cosx)#? How do you differentiate #e^(2x^2+x) # using the chain rule? How do you differentiate #f(x)=(sin^3x^2))^(3/2)# using the chain rule? Indeed, we have So we will use the product formula to get Caculus question on finding deriavatives? How do you find the derivative of the function #f(x)=sqrt(1+2x)#? How do you find the derivative of #cos(1-2x)^2#? If #f(x)= tan5 x # and #g(x) = 2x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)= ln(x^2)#? If you still don't know about the product rule, go inform yourself here: the product rule. How do you differentiate #3sin^2(3x) # using the chain rule? How do you find the derivative of # pi^(x+2)# using the chain rule? What is the second derivative of # (x^2 + 1/x)^5#? How do you find the derivative of #(arctan x)^3#? What is the derivative of #Ln(ln(ln(2x)))#? How do you differentiate #y= -cos^-1 (1/x^5)#? The chain rule can be thought of as taking the derivative of the outer function (applied to the inner function) and multiplying it times the derivative of the inner function. What is the derivative of #y = xsinh^-1(x/3)-(sqrt(9+x^2))#? bookmarked pages associated with this title. How do you differentiate #f(x)=sqrt(xsin(ln(x)^3)# using the chain rule? How do you find the derivative of #f(x) = e^x + e^(-x / 2)#? How do you differentiate #f(x)=csc(e^x) # using the chain rule? y = f(u) and u = g(x) and both dy/du and du/dx exists, then the derivative of the function . How do you differentiate #f(x)=sec(1/sqrt(3x^2-4) ) # using the chain rule? How do you differentiate #f(x)=ln(sinx)^2/(x^2ln(cos^2x^2))# using the chain rule? How do you find the first and second derivative of #y=x^(e^cx)#? How do you find the derivative of #(ln tan(x))^2#? This is for both equations. How do you differentiate #f(x)=sec^4(x^3-x^2 ) # using the chain rule? It’s also one of the most important, and it’s used all the time, so make sure you don’t leave this section without a solid understanding. How do you find the derivative of #x^lnx#? How do you differentiate #f(x)=ln(x^2)# using the chain rule? This is the final formula that we use in backpropagation. Let's see what that looks like mathematically: Chain Rule: #f'(g(x))*g'(x)# How do you use the chain rule to differentiate #y=(x^2+1)^(1/2)#? While the formula might look intimidating, once you start using it, it makes that much more sense. How do you use the chain rule to differentiate #2^(-9z^2+3z+5)#? What is #h'(3)#, where #h(x)= (f(x) +g(x))^2#? How do you use the chain rule to differentiate #root9(-cosx)#? How do you find the derivative of #y = cos^3(3x+1)#? How do you differentiate #f(x) =x(x+3)^3?# using the chain rule? If #f(x) = -x^2 -2x# and #g(x) = e^(x)#, what is #f'(g(x)) #? How do you find the derivative of #4/sqrt x#? How do you use the chain rule to differentiate #y=(5x^4+1)^2#? If #f(x)= csc 3 x # and #g(x) = sqrt(2x-3 #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=e^(cossqrtx)# using the chain rule.? What is the derivative of #(x^2 + 1/x)^5#? If #f(x)= sqrt(x^2-1 # and #g(x) = 1/x #, what is #f'(g(x)) #? How do you differentiate #f(x)=sec(-e^(sqrtx) ) # using the chain rule? What is the derivative of #f(x) = x^(5/2) #? How do you differentiate #f(x)=1/sqrtsec(e^(x) ) # using the chain rule? How do you find the derivative of # 1/[16x+3]^2# using the chain rule? How do you use the chain rule to differentiate #1/ln(4x)#? The only problem is that we want dy / dx, not dy /du, and this is where we use the chain rule. What is the derivative of #sin^2(x) + sinx#? Here z is the function of y, z = f(y) and y is a function of x, y= g(x) Using the previous formula, we can rewrite the differential equation as follows: Let us understand this better with the help of an example. How do you differentiate #f(x) = ln(1/sqrt(arcsin(e^(x)) ) ) # using the chain rule? How do you differentiate #f(x) = (1-sqrt(3x-1))^2 # using the chain rule? How do you use the chain rule to differentiate #y=(5x^3-3)^5root4(-4x^5-3)#? How do you differentiate #f(x)=csc(sqrt(x)) # using the chain rule? Use the chain rule twice?? How do you differentiate # f(x)=1/sqrt(ln(xe^x))# using the chain rule.? How do you differentiate #tan(cos^3(x))#? How do you differentiate #f(x) = (5x-4 )^(2) # using the chain rule? How do you differentiate #f(t)=tan(e^t)+e^(tant)#? How do you find the derivative of #f(x) = -5 e^{x \cos x}# using the chain rule? What is the derivative of #sqrt(4x² + 1)#? How do you use the chain rule to differentiate #f(x)=sin(cos(tan(x^3+sin(x^2))))#? How do you differentiate #f(x)=arccos(tan(1/(1-x^2)) )# using the chain rule? What is the derivative of #sqrt(t^5) + root(4)(t^9)#? How do you use the chain rule to differentiate #y=sin^2(cos(4x))#? How do you find the derivative of #sqrt(x^2+2x-1)#? How do you find the derivative of #sqrt(x - 2)#? How do you differentiate #f(x) = sqrt((5x+1)^2+(2x-1))# using the chain rule? How do you use the chain rule to differentiate #r=sec2thetatan2theta#? What is the derivative of #ln[(x(x^2+1)^2)/(2x^3-1)^(1/2)] #? How do you use the chain rule to differentiate #f(x)=sqrt(sqrt(5x^3-sec(x^2-1))#? How do you find the derivative of #(x^2+x)^2#? How do you differentiate #y = (2x+3)^4 / x#? So all we need to do is to multiply dy /du by du/ dx. How do you find dy/dx given #y=ln(2+x^2)#? y = tan^4(3x)#? What is the derivative of #cos[sin^-1 (2w)]#? How do you find the derivative of #f(x) = sin x + 1/2 cot x#? How do you differentiate #f(x)=(1/(x-3)^2)^2# using the chain rule? How do you use the chain rule to differentiate #(-cosx)^2008#? How do you find the second derivative of #y=Acos(Bx)#? What is the derivative of #f(x) = cos (x^2 - 4x)#? However, we rarely use this formal approach when applying the chain rule to … How do you find the derivative for #f(x)= x(1-x)^3#? How do you find the derivative of #f(x)= (x+sinx)/(cosx) #? How do you differentiate #sqrt(4x² + 1)#? What is the derivative of #sin(x^2+5) cos(x^2+9x+2)#? How do you differentiate #f(x)=sqrt(x-(3x+5)^2)# using the chain rule.? Most problems are average. How do you find the second derivative of #y=x^5#? How do you differentiate #f(x)=e^(4x ln(xsin^2x)# using the chain rule? What is the derivative of #x^3 * (2/3x^2 -1)^4#? How do you find the derivative of # y= ln (1 - x^2)#? How do you find the derivative of #y=3/4(x^(2)-1)^(2/3)#? How do you use the chain rule to differentiate #y=(2x-7)^3#? How do you differentiate #f(x)=sin(6x+5x^2+1)# using the chain rule? How do you differentiate #f(x)= (4x^5+5)^(1/2)# using the chain rule? Answer to 2: Differentiate y = sin 5x. How do you differentiate #y=3cot(ntheta)#? If #f(x) =-e^(2x-1) # and #g(x) = -3sec^2x^2 #, what is #f'(g(x)) #? How do you differentiate #f(x)=cos(tanx)# using the chain rule? How do you use the chain rule to differentiate #f(x)=ln(cosx)#? How do you use the chain rule to differentiate #y=4(x^2+1)^2#? How do you find the derivative of #y= sin{cos^2(tanx)}#? Let f be a function of g, which in turn is a function of x, so that we have f(g(x)). How do you differentiate #y = (x^3 + 2)^2(x^5 + 4)^4#? How do you differentiate #f(x)=tan((e^x)^2)# using the chain rule? How do you find the derivative of #ln sqrt (x^2-4)#? The chain rule applies whenever you have a function of a function or expression. How do you differentiate #f(x)=-cos(sqrt(1/(x^2))-x)# using the chain rule? How do you differentiate #f(x)=(x^3-2x+3)^(3/2)# using the chain rule? How do you find the derivative of #(cosx)(sinx)#? Chain rule is also often used with quotient rule. How do you find the derivative of the function # The chain rule tells us how to find the derivative of a composite function. How do you differentiate # y = 2/[(e^(x) + e^(-x)]#? What is the derivative of #ln(sqrt(sin(2x)))#? How do you find the derivative of # ln(x+1)#? How do you use the chain rule to differentiate #-cos(4x+9)#? How do you use the chain rule to differentiate #y=x^2tan(1/x)#? How do you differentiate #f(x)=e^(-x^2-2x+1) # using the chain rule? How do you find the derivative of #f(x) = -15 / (4x + 5)^4# using the chain rule? If , where u is a differentiable function of x and n is a rational number, then Examples: Find the derivative of each function given below. For instance, if you had sin(x^2 + 3) instead of sin(x), that would require the chain rule. How do you find the derivative of #y = cos(a^3 + x^3)# using the chain rule? How do you find the derivative of #h(x)= 1/(6x^2+x+1)^2#? How do you find the derivative of #y=tan(5x)# ? How do you differentiate #f(x)=root4(1+2x+x^3)#? How do you use the chain rule to differentiate #y=sec^4x#? How do you find the second derivative of #y=e^(-pix)#? What is the derivative of #sin(x^2 -2)^3#? How do you find the derivative of #f(x)=(5x^6sqrt x) + (3/(x^3 sqrt x))#? How do you use the chain rule to differentiate #y=cos(sqrt(8t+11))#? How do you use the chain rule to differentiate #sqrt(-cosx)#? How do you differentiate #y=sqrt(4x +3)#? How do you find the derivative of #r(x)= (0.3x-4.9x^-1)^0.5#? How do you use the chain rule to differentiate #y=sin4x^3#? How do you use the chain rule to differentiate #y=cos(2x+3)#? How do you differentiate #y= (2e^x) / (1+e^x) #? How do you use the chain rule to differentiate #y=root4(-3x^4-2)#? What is the derivative of # x * ((4-x^2)^(1/2))#? How do you differentiate #f(x)= 1/2 sin(2x) + cosx#? How do you differentiate #f(x)=cos(e^(3x^2)+7) # using the chain rule? What is the derivative of #g(t)=(pi)(cos t - 1/t^2)#? To illustrate this, if we were asked to differentiate the function: What are the first two derivatives of #1/ln(x)#? The chain rule gives us that the derivative of h is . How do you differentiate #f(x)=tane^(4x)# using the chain rule.? How do you differentiate #f(x) = sqrt((3x)/(2x-3))# using the chain rule? Before using the chain rule, let's multiply this out and then take the derivative. How do you find the derivative of # y=x^3(7x-7)^5# using the chain rule? What is the derivative of #cos^4(x)-sin^4(x)#? Before we actually do that let’s first review the notation for the chain rule for functions of one variable. How do you differentiate #f(x)=cose^(4x)# using the chain rule.? The chain rule is arguably the most important rule of differentiation. How do you differentiate #f(x) = sqrt(sin^3(4-x) # using the chain rule? How do you use the chain rule to differentiate #y=tan(x^2)+tan^2x#? How do you use the chain rule to differentiate #log_13(-cosx)#? How do you differentiate #f(x)=4(x^2 + x - 1)^10 # using the chain rule? How do you differentiate #f(x)=sec(8x ) # using the chain rule? How do you differentiate #f(x)=csc(5x) # using the chain rule? How do you differentiate #f(x)=sin((x/(x^2-1))^(3/2))# using the chain rule? How do you differentiate #f(x)=ln(cos(e^(x) )) # using the chain rule? The chain rule can be thought of as taking the derivative of the outer function (applied to the inner function) and multiplying it times the derivative of the inner function. How do you differentiate # f(x)=e^sqrt(3lnx+x^2)# using the chain rule.? Instead, we use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. How do you find the derivative of #f(t)=80-4.9t^2#? How do you determine #(dy)/(dx)# given #y=sec(sqrt(x^3+x))#? How do you use the chain rule to differentiate #y=sinroot3(x)+root3(sinx)#? How do you find the derivative of #x/ sqrt (x^2 +1)#? How do you differentiate #f(x)=1/sec(e^(x) ) # using the chain rule? How do you find the derivative of #y= sin(xcosx)#? How do you find the derivative of # f(t)=sin^2[e^(sin^2)t]# using the chain rule? How do you differentiate #f(x)=sin e^(4x)# using the chain rule.? How do you find the derivative of #sqrt(3x)#? Can you apply the chain rule when determining the second derivative of a function? How do you differentiate #y = 6 cos(x^3 + 3)#? How do you find the derivative of #cos(pi*x^2)#? What is the derivative of # y= ln(2x)/x^2#? Thus use the chain rule to show that the canonical form is U ξη = 0 where U (ξ, η) = u (x (ξ, η), y (ξ, η)). Proof of the chain rule. How do you differentiate # f(x)= (3e^x+2)^3 # using the chain rule.? How do you differentiate #f(x)=x/arcsinsqrt(ln(1/x^2)# using the chain rule? If #f(x)= x^2-x # and #g(x) = x^( 1/3 ) #, what is #f'(g(x)) #? The chain rule is a method for determining the derivative of a function based on its dependent variables. How do you find the derivative of #cos^2(x^2-2)#? How do you differentiate #arcsin(sqrt(sin^2(1/x) )# using the chain rule? How do you differentiate #f(x)=cot(sqrt(x^2-1)) # using the chain rule? How do you differentiate #f(x)=(ln(sinx)^2/(x^2ln(cos^2x^2)# using the chain rule? How do you differentiate #f(x)=x/ln(sqrt(1/x))# using the chain rule? and any corresponding bookmarks? How do you differentiate # f(x)= sin(x-2)^3 # using the chain rule.? How do you differentiate #f(x)=(2x-cos^3x)^2-(lnx)^2# using the chain rule? How do you find the derivative of #f(x)=2/(6x+5x+1)^2#? Example. How do you differentiate #tan(3x^2) - csc ( ln(4x) )^2#? How do you differentiate #f(x)=(x^2-2x)^2# using the chain rule? Steps for using chain rule, and chain rule with substitution. The composition of two functions [math]f[/math] with [math]g[/math] is denoted [math]f\circ g[/math] and it's defined by [math](f\circ g)(x)=f(g(x)). How do you differentiate #f(x)=(sin(tanx))^3#? How do you find the derivative of # cos(1-2x)^2#? If #f(x)= tan8 x # and #g(x) = e^(-3x ) #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #y = ln(x^(1/2))#? If #f(x) =cos3x # and #g(x) = sqrt(3x-1 #, what is #f'(g(x)) #? How do you differentiate #y = (sin(3x) + cot(x^3))^8#? What is the derivative of #sin(x(pi/8))#? How do you find the derivative of #ln^2 x#? How do you differentiate #y=(6x^2 + 2x)^3#? from your Reading List will also remove any Brush up on your knowledge of composite functions, and learn how to apply the chain rule correctly. How do you differentiate #f(x)=e^(4^(1/(x^2)))# using the chain rule? The following three problems require a more formal use of the chain rule. If #f(x) =-sqrt(2x-1) # and #g(x) = 3/x^3 #, what is #f'(g(x)) #? How do you differentiate # y=cos^-1(1-2x^2)#? What is the derivative of #T(w)=cot^3(3w+1)#? If #f(x)= cot5 x # and #g(x) = sqrt(-x+3 #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=sec^2x-tan^2x#? How do you differentiate # f(x) = tan(sinx)#? How do you differentiate #y=(x^4+3x^2-2)^5#? How do you find the derivative of #y=arcsin(5x+5)#? How do you find the derivative of #f(x)=5e^x#? What is the derivative of # (ln (x-4)) ^ 3#? How do you find the derivative of # ln[x]/x^(1/3)#? (x+1) but it will take longer, and also realise that when you use the product rule this time, the two functions are 'similiar'. How do you use the chain rule to differentiate #y=((x+1)/(x-2))^5#? How do you use the chain rule to differentiate #y=3(5x+5)^5#? What is the derivative of #1/(1 + x^4)^(1/2)#? How do you differentiate #y=sqrt( (x-1) (x-2) (x-3))#? Use the Chain Rule to find the derivatives of the following functions, as given in Example 59. How do you differentiate #f(x)=e^cos(-2lnx)# using the chain rule? How do you use the chain rule to differentiate #root3(4x+9)#? Using the point-slope form of a line, an equation of this tangent line is or . How do you find the derivative of #f(x)=1/(2x+5)^5#? If #f(x)= cos(-2 x -1) # and #g(x) = 3x^2 -5 #, how do you differentiate #f(g(x)) # using the chain rule? The chain rule is used when you want to differentiate a function to the power of a number. If # A = 9/16(4r-sin(4r)) # and #(dr)/dt=0.7# when #r=pi/4# then evaluate # (dA)/dt # when #r=pi/4#? Alternatively, by letting h = f ∘ g, one can also … If #f(x)= sec 4 x # and #g(x) = 2 x #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate # f(x) = (x - 1)^4 /(x^2+2x)^5# using the chain rule? How do you differentiate #f(x) = x/sqrt(sin^2(1+x^2) # using the chain rule? What is the derivative of #f(x)= 2^(3x)#? How do you use the chain rule to differentiate #f(x)=sin(x^2)/(x^4-3x)^4#? What is the derivative of #3*(sqrt x) - (sqrtx^3)#? How do you find the derivative of #sqrt(x+1)#? How do you find the derivative of # sin^2(x/6)#? How do you differentiate #f(x) = 1/sqrt(arctan(2x^3) # using the chain rule? How do you differentiate # y=sec (x^2/pi - xpi)# using the chain rule? How do you find the derivative of #f(x)=ln(ln(7x))+ln(ln6)#? How do you find the derivative of #x^(3/x)#? How do you differentiate #f(x)=ln(sqrt(sin(x^2-3x)))# using the chain rule? How do you find the second derivative of #y=1/x#? How do you find the derivative of #f(x) = e^x + e^-x / 2 #? How do you differentiate #y= 3 / (sqrt(2x+1)#? How do you find the derivative of #y=x*sqrt(16-x^2)#? How do you differentiate #f(x)=e^(secsqrtx)# using the chain rule.? How do you differentiate #f(x)=sec(1/sqrt(3x) ) # using the chain rule? 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