Question

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

Answer 1

`d/dxe^(2x^2+2x)=(4x+2)e^(2x^2+2x)`

Explanation:

This problem will require an application of the Chain Rule which, when applied to `e` raised to the power of some function `u,` tells us that

`d/dxe^u=e^u*(du)/dx`

Here, `u=2x^2+2x,` so we have

`d/dxe^(2x^2+2x)=e^(2x^2+2x)*d/dx(2x^2+2x)`

`d/dx(2x^2+2x)=4x+2`, so we end up with

`d/dxe^(2x^2+2x)=(4x+2)e^(2x^2+2x)`