Question

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

Answer 1

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 $g'(x)=(2x+2)e^{x^2+2x}+3$

Answer 2

$g(x)=e^{x^2+2x}+3x\\ g'(x)=e^{x^2+2x}\cdot(2x+2)+3\\ g'(x)=2e^{x^2+2x}(x+1)+3$