How do you find the derivative of y=xe^x?

Mar 4, 2018

The derivative of y = $x {e}^{x}$ is y' = ${e}^{x} + x {e}^{x}$

Explanation:

Use the product rule (u'v + v'u) to calculate the derivative:

First, write the values of u, u', v and v':

u = $x$
u' = 1
v = ${e}^{x}$
v' = ${e}^{x}$

Next, substitute these values into the product formula:

(u'v + v'u)

(1 x ${e}^{x}$) + (${e}^{x}$ x $x$) = ${e}^{x}$ + $x {e}^{x}$