# How do you calculate the derivative of the function f(x)=e^x(x^2 + 1)?

##### 1 Answer
Feb 25, 2015

The answer is:

$y ' = {e}^{x} \left({x}^{2} + 1\right) + {e}^{x} \cdot 2 x = {e}^{x} \left({x}^{2} + 1 + 2 x\right) = {e}^{x} {\left(x + 1\right)}^{2}$

This is because the rule says:

$y = f \left(x\right) \Rightarrow y ' = f ' \left(x\right) \cdot g \left(x\right) + f \left(x\right) g ' \left(x\right)$.