Question

How do you differentiate `f(x)=x(lnx)^3` using the product rule?

Answer 1

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

Explanation:

`f=x,g=(lnx)^3`
`f'=1,g'=3(lnx)^2*1/x`
`f'(x)=fg'+gf'=x*(3(lnx)^2)/x +(ln x)^3`
`f'(x)=3(lnx)^2+(lnx)^3`