Question

How do you find the derivative of `f(x) = x^3e^x`?

Answer 1

`f'(x) = 3x^2e^x + x^3e^x`

Explanation:

You need to use the product rule; `d/dx(uv)=u(dv)/dx+v(du)/dx`

`f(x)=x^3e^x`
`:. f'(x) = x^3d/dxe^x + e^xd/dxx^3`
`:. f'(x) = x^3e^x + e^x(3x^2)`
`:. f'(x) = 3x^2e^x + x^3e^x`