Question

Given the following functions: f(x)=cos(x) and g(x)=(x^8)+1. Find [d/dx] g(f(x))

Answer 1

\[(g\circ f)'=g'(f)f'\] so you get
\[g\circ f(x)=g(f(x))=g(\cos(x))=\cos^8(x)+1\] and
\[\frac{d}{dx}\cos^8(x)+1=8\cos^7(x)\times -\sin(x)=-8\sin(x)\cos^7(x)\]