find g " (x) for g(x) = x^2ln x

Calculus
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find g " (x) for g(x) = x^2ln x

Jun 24th, 2015

Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

we have :  g(x) = x²ln(x) 

so : g'(x) = (x²)'ln(x) + (x²)(ln(x))' = 2xln(x) + x²/x = 2xln(x) + x 

and :  g"(x) = (2xln(x) + x)' =  ((2x)'ln(x) + 2x(ln(x))' + x' ) = ( 2ln(x) + 2x(1/x) + 1) = 2ln(x) + 2 + 1 = 2ln(x) + 3


so :  g"(x) = 2ln(x) + 3


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Please let me know if you need any clarification. I'm always happy to answer your questions.Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 24th, 2015

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