How do you differentiate x(lnx)^2?

1 Answer
Jun 9, 2016

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 ]