# How do you use the product rule to find the derivative of y=(x^3+2x)*e^x ?

Jul 27, 2014

Answer, $y ' = {e}^{x} \cdot \left({x}^{3} + 3 {x}^{2} + 2 x + 2\right)$

Explanation :

Using Product Rule (which is also explained in the following problem) to solve this problem,

$y ' = \left({x}^{3} + 2 x\right) \cdot \left({e}^{x}\right) ' + {e}^{x} \left({x}^{3} + 2 x\right) '$

$y ' = \left({x}^{3} + 2 x\right) \cdot {e}^{x} + {e}^{x} \left(3 {x}^{2} + 2\right)$

$y ' = {e}^{x} \cdot \left({x}^{3} + 3 {x}^{2} + 2 x + 2\right)$