Question

How do you differentiate `f(x)=xe^x` using the product rule?

Answer 1

`f'(x) = e^x(x+1)`

Explanation:

Using the product rule, together with the derivatives

• `d/dxx = 1`
• `d/dxe^x = e^x`

we get

`f'(x) = d/dxxe^x`
`= x(d/dxe^x) + (d/dxx)e^x`
`= xe^x+e^x`
`= e^x(x+1)`