Answer
inside: g(x)=$6e^2-4x^5$
outside: f(g)=$6g^{1/3}$
derivative: f'(x)=$(-20/3)x^4(6e^2-4x^5)^{-2/3}$
Work Step by Step
Use the chain rule to take the derivative $\frac{df(g(x))}{dx}=f'(g(x))g'(x)$
To find the inside, you take the function inside the parenthesis.
To find the outside, you exchange the parenthesis to a variable.
Then take its derivative and put it together.