What is the derivative of #f(x)=sin(lnx)#?

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What is the derivative of #f(x)=sin(lnx)#?

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Answer 1 · 2015-11-11T20:24:11

#f'(x)=cos(ln(x)) * 1/x#

Explanation:

Use the facts that #d/dx(sin(x))=cos(x)#, #d/dx(ln(x))=1/x#, and the Chain Rule: #d/dx(f(g(x)))=f'(g(x)) * g'(x)# with #f(x)=sin(x)# and #g(x)=ln(x)#.

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What is the derivative of #f(x)=sin(lnx)#?

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