Question

How do you differentiate `f(x) = x² ln(x)`?

Answer 1

`f'(x)=2xlnx+x`

Explanation:

Use product rule: if

`f(x)=g(x)h(x)`, then

`f'(x)=g'(x)h(x)+g(x)h'(x)`

So,

`g(x)=x^2`
`h(x)=lnx`

and

`g'(x)=2x`
`h'(x)=1/x`

Put this all together:

`f'(x)=2x(lnx)+x^2(1/x)`

`=>2xlnx+x`