Answer:
[tex]y' = xe^{x}(2 + x)[/tex]
Step-by-step explanation:
If we have a product function y, in the following format
[tex]y = f(x)*g(x)[/tex]
This function has the following derivative
[tex]y' = f'(x)*g(x) + g'(x)*f(x)[/tex]
In this problem, we have that:
[tex]y = x^{2}e^{x}[/tex]
So
[tex]f(x) = x^{2}, f'(x) = 2x, g(x) = e^{x}, g'(x) = e^{x}[/tex]
The derivative of the function is:
[tex]y' = f'(x)*g(x) + g'(x)*f(x)[/tex]
[tex]y' = 2xe^{x} + x^{2}e^{x}[/tex]
[tex]y' = e^{x}(2x + x^{2})[/tex]
[tex]y' = xe^{x}(2 + x)[/tex]
