chain rule twice

Calculus Tutorial

chain rule twice

Intro

The chain rule tells us how to take the derivative of their composition.
d/dx(f(g(x)))=f'(g(x)).g'(x)

Sample Problem

y=(cos(x3))2
find dy/dx

Solution

y=(cos(x3))2
dy/dx=2cos(x3).d/dx(cosx3) chain rule

d/dx(cosx3)=-sinx3.d/dx(x3) chain rule

d/dx(x3)=3×2 power rule

dy/dx=2cosx3.(-sinx3).3×2
=-6x2cosx3.sinx3



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