Question

Differentiating Exponential Functions In Exercise, find the derivative of the function. y = x2ex

Answer 1

Answer:

$y' = xe^{x}(2 + x)$

Step-by-step 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:

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

$y' = 2xe^{x} + x^{2}e^{x}$

$y' = e^{x}(2x + x^{2})$

$y' = xe^{x}(2 + x)$