Question

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

Answer 1

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\[\frac{d}{dx}\log y=\frac{d}{dx}\cos x \log x \rightarrow \frac{d \log y}{dy}\frac{dy}{dx}=\frac{d}{dx}\cos x \log x\]\[\rightarrow \frac{1}{y}\frac{dy}{dx}=\cos x \frac{1}{x}+\log x (-\sin x)\]\[\rightarrow \frac{dy}{dx}=y(\frac{\cos x}{x}-\sin x \log x)\]\[=x^{\cos x}(\frac{\cos x }{x}-\sin x \log x)\]

Answer 2

log == ln

Answer 3

omg ty!!!!

Answer 4

you're welcome

Answer 5

become a fan ;)

Answer 6

is that diff eq?

Answer 7

Those sort of problems are part of calc2

Answer 8

really? ive never heard of logarithmic diferentiation O.o