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

1 Answer

Himanshu Shekhar

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 ] #

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