Understanding how to set up g(f(x)) comparatively to f(g(x)) The question reads: > Given the following functions: $f(x)=\cos(x)$ and $g(x)=x^{7}+1$, find: > > * **a:** $\displaystyle \frac{d}{dx} f(g(x)) = ?$ > * **b:** $\displaystyle \frac{d}{dx} g(f(x)) = ?$ > For **(a)** , I obtained: $\cos x(x^7+1) \longrightarrow$ derivative $-\sin(x^7+1)(7x) \longrightarrow -7x \sin(x^7+1)$. However, for **(b)** I am having a problem understanding. Am I suppose to set it up as $x^{7}+1(\cos x)$ or $\cos^{7}+1$?

For part b, it says your _f(x)_ needs to be on the inside and _g(x)_ needs to be on the outside.

Your second answer is right, because you would then replace the _x_ with cos, so you would get cos^7 +1