Question

Differentiating Exponential Functions In Exercise, find the derivative of the function.

y = x2ex

Answer 1

`y' = xe^(x)(2 + x)`

Explanation:

If we have a product function y, in the following format

`y = f(x)*g(x)`

This function has the following derivative

`y' = f'(x)*g(x) + g'(x)*f(x)`

In this problem, we have that:

`y = x^(2)e^(x)`

So

`f(x) = x^(2), f'(x) = 2x, g(x) = e^(x), g'(x) = e^(x)`

The derivative of the function is:

`y' = f'(x)*g(x) + g'(x)*f(x)`

`y' = 2xe^(x) + x^(2)e^(x)`

`y' = e^(x)(2x + x^(2))`

`y' = xe^(x)(2 + x)`