chain rule

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(e(x3+x))
find dy/dx

Solution

y=cos(e(x3+x))
u(x)=e(x3+x) difine u(x)
y=cos(u) express y in term of u
dy/dx=dy/du.du/dx chain rule
dy/dx=d/du(cos(u)).d/dx(e(x3+x)) substitute y(u) and u(x)
dy/dx=-sin(u).e(x3+x).(3×2+1) evaluate derivative
dy/dx=-sin(e(x3+x)).e(x3+x).(3×2+1) substite u in term of x



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