Logarithmic differentiation

  • Thread starter crybllrd
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  • #1
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Homework Statement



Find y' using logarithmic differentiation if [tex]y=x^{sin(x)}[/tex]

Homework Equations





The Attempt at a Solution



[tex]lny=sin(x)ln(x)[/tex]

[tex]\frac{1}{y}(y')=sin(x)(\frac{1}{x})+ln(x)\cdot cos(x)[/tex]

[tex](y')=[sin(x)(\frac{1}{x})+ln(x)\cdot cos(x)]y[/tex]

Did I do this one properly?
Thanks in advance.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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It looks fine to me.
 
  • #3
jhae2.718
Gold Member
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Looks good to me.

Depending on what the question wants, you may want to sub in [tex]x^{\sin(x)}[/tex] for [tex]y[/tex] in your final answer. (LaTeX tip: you can use \sin, \cos, and \ln to get "normal" text for sin, cos, ln, etc.)
 

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