Question

Find f'(x) if f(x) = (2/(x^1/3)) + 3 cos x + x^pi

Answer 1

The derivative of
`f` is

`f'(x)=\left(2x^(-1/3)+3\cos x+x^\pi\right)'`

`f'(x)=\left(2x^(-1/3)\right)'+(3\cos x)'+\left(x^\pi\right)'`

By the power rule,

`f'(x)=-\frac23x^(-4/3)+(3\cos x)'+\pi x^(\pi-1)`

The derivative of
`\cos x` is
`-\sin x`:

`f'(x)=-\frac23x^(-4/3)-3\sin x+\pi x^(\pi-1)`