anonymous
  • anonymous
Use logarithmic differentiation to find the derivative of the function. y = x^(cos x)
Mathematics
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anonymous
  • anonymous
Use logarithmic differentiation to find the derivative of the function. y = x^(cos x)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Take the logarithm of both sides to get,\[\log y = \log x^{\cos x} \rightarrow \log y = \cos x \log x\]Then, taking the derivative of both sides, you get\[\frac{d}{dx}\log y=\frac{d}{dx}\cos x \log x \rightarrow \frac{d \log y}{dy}\frac{dy}{dx}=\frac{d}{dx}\cos x \log x\]\[\rightarrow \frac{1}{y}\frac{dy}{dx}=\cos x \frac{1}{x}+\log x (-\sin x)\]\[\rightarrow \frac{dy}{dx}=y(\frac{\cos x}{x}-\sin x \log x)\]\[=x^{\cos x}(\frac{\cos x }{x}-\sin x \log x)\]
anonymous
  • anonymous
log == ln
anonymous
  • anonymous
omg ty!!!!

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anonymous
  • anonymous
you're welcome
anonymous
  • anonymous
become a fan ;)
anonymous
  • anonymous
is that diff eq?
anonymous
  • anonymous
Those sort of problems are part of calc2
anonymous
  • anonymous
really? ive never heard of logarithmic diferentiation O.o

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