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anonymous
 5 years ago
Use logarithmic differentiation to find the derivative of the function.
y = x^(cos x)
anonymous
 5 years ago
Use logarithmic differentiation to find the derivative of the function. y = x^(cos x)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Take 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
 5 years ago
Best ResponseYou've already chosen the best response.0Those sort of problems are part of calc2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0really? ive never heard of logarithmic diferentiation O.o
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