Question

How do you differentiate `x(lnx)^2`?

Answer 1

Use the product rule and simplify.
`d/dx [ x * ln^2(x) ] = ln(x) [ ln(x) +2 ]`

Explanation:

`d/dx [ x * ln^2(x) ]`

`= (d/dx [ x ]* ln^2(x)) +( x * d/dx [ ln^2(x) ] )`

`= (1* ln^2(x)) +( x * d/dx [ ln(x) ] * 2 ln(x))`

`= ( ln^2(x)) +( x * 1/x * 2 ln(x))`

`= ( ln^2(x)) +(2 ln(x))`

`= ln(x) [ ln(x) +2 ]`