Question

Derivative help please!

What is the derivative of:
y=xtanh^-1(x)+ln(sqrt(1-x^2))

Answer 1

Use the product rule on each term.

derivative of arctanhx: http://math.info/Calculus/Derivatives_Hyp_InvHyp/

A little hard to read, but I don't want to put it all into latex: http://answers.yahoo.com/question/index?qid=20111013224713AAwf64s

Answer 2

I understand the xtanh^-1 part but I'm still screwing up my work with the ln part mind helping me there? (I'm trying to do that work so I learn instead of just copying an answer)

Answer 3

Derivative of ln(f(x)) is \[\large \frac{ d }{dx } \ln u = u' \frac{ 1}{ u }\]

So find the derivative of the inside function of ln(sqrt(1-x^2)), and multiply it by 1/(inside function)

Answer 4

\[\LARGE \frac{ d }{dx } \ln \sqrt{1-x^2} =\frac{ d }{dx } \left( \sqrt{1-x^2} \right) \frac{ 1 }{ \sqrt{1-x^2}}\]

Answer 5

All you gotta do is find \[\LARGE \frac{ d }{dx } (1-x^2)^{\frac{ 1 }{ 2 }} = \]

Answer 6

so then the derivative of ln(sqrt(1-x^2)) would be -x/(1-x^2) right?

Answer 7

Correct.

Answer 8

Thank you very much for your help. Would you possibly be able to help with one last problem? I'll throw up a new question for it