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

1. 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)$

2. anonymous

log == ln

3. anonymous

omg ty!!!!

4. anonymous

you're welcome

5. anonymous

become a fan ;)

6. anonymous

is that diff eq?

7. anonymous

Those sort of problems are part of calc2

8. anonymous

really? ive never heard of logarithmic diferentiation O.o