Question

What is the derivative of g(x)=e^(x^2+2x)+3x

Answer 1

`g(x)=e^(x^2+2x)+3x\\ g'(x)=e^(x^2+2x)\cdot(2x+2)+3\\ g'(x)=2e^(x^2+2x)(x+1)+3`

Answer 2

Ok first we can split it in two :
`e^(x^2+2x)` and
`3x`.

The derivative of
`3x` is 3.

For the first part, we use the chain rule :
`[f(g(x))]'=g'(x)f'(g(x))` hence
`(e^(x^2+2x))'=(x^2+2x)'e^(x^2+2x)` (since the derivative of the exponential is itself) hence
`g'(x)=(2x+2)e^(x^2+2x)+3`