Question

How do you find the derivative of `y=e^((4x^3+5)^2)`?

Answer 1

`y' = 24x^2(4x^3+5)e^((4x^3+5)^2)`

Explanation:

If `y=e^(f(x))`, then `y'=f'(x)e^(f(x))`

In order to differentiate `f(x)`, we must use the chain rule, `[f(x)]^n=n[f(x)]^(n-1)f'(x)`

`f'(x)=2(4x^3+5)12x^2=24x^2(4x^3+5)`

So `y' = 24x^2(4x^3+5)e^((4x^3+5)^2)`