given,
y = x^3e^x
to get the derivative of this function, we will have to use product rule.
product rule: d/dx (uv) = u dv/dx + v du/dx
so,
y = x^3e^x
y'(x) = x^3 d/dx e^x + e^x d/dx x^3
y'(x) = x^3e^x + e^x (3x^2)
therefore,
y'(x) = 3x^2 e^x + x^3 e^x
so,
the derivative of the function y = x^3e^x is
= 3x^2 e^x + x^3 e^x