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Chain Rule

TNT Week 3 Assignment

QuestionAnswer
What is the chain rule? How to take the derivative involving composition of functions.
d/dx [f(g(x))] = ? f'(g(x))*g'(x)
If y=f(u) and u is a function of x, what is y' ? y' = f'(u) * du/dx
Do you need to use the chain rule for: d/dx [ e^x + 3x]? No
Do you need to use the chain rule for: d/dx [sin(2x)] ? Yes
Do you need to use the chain rule for: d/dx [ (3x + cos(x))^2] Yes
What is d/dx [u^n] if u is a function of x and n is not equal to zero? n*u^(n-1)*du/dx
If f(x)=x^2 and g(x)=sin(x), and h(x)=f(g(x)), find h'(x) 2(sin(x))*cos(x)
If h(x)=g(f(x)), f'(4)=6, f(4)=7, g'(7)=2, find h'(4) 12
Created by: james.metzinger
 

 



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