Question

How do you find the derivative of `f(x) = x^(5/ 2) e^x`?

Answer 1

`f'(x)=x^(5/2)e^x +5/2 x^(3/2)e^x`

Explanation:

Let `f=x^(5/2), g=e^x`
`f'=5/2 x^(3/2), g'=e^x`
`f'(x)=fg'+gf'`
`f'(x)=x^(5/2)e^x +5/2 x^(3/2)e^x`