# Find f'(x) for {eq}f(x) = (e^{x^3} - 3)^4 {/eq}

## Question:

Find f'(x) for {eq}f(x) = (e^{x^3} - 3)^4 {/eq}

## Chain Rule:

The chain rule is expressed as {eq}\dfrac{\mathrm{d} }{\mathrm{d} x}(f(g(x)))=f'(g(x))g'(x) {/eq}. By applying the chain rule, we'll evaluate the derivative of the composite function. For example, {eq}\tan (x^2) {/eq} is a composition of two functions {eq}\tan (x) {/eq} and {eq}x^2 {/eq}.

Become a Study.com member to unlock this answer!

We have to find {eq}f'(x){/eq} for {eq}f(x) = (e^{x^3} - 3)^4 {/eq}. Differentiate the given function with respect to {eq}x{/eq}.

\begin{align} f...