what is the derivative of (ln(3))^cosx

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- Oct 21st 2008, 07:25 PMjojoferni244derivative
what is the derivative of (ln(3))^cosx

- Oct 21st 2008, 07:28 PMJhevon
- Oct 22nd 2008, 01:04 AMProve It
Let $\displaystyle u = \cos{x}$ so $\displaystyle y = \ln{3}^u$

$\displaystyle \frac{du}{dx} = -\sin{x}$ and $\displaystyle \frac{dy}{du} = \ln{3}^u\ln{\ln{3}} = \ln{3}^{\cos{x}}\ln{\ln{3}}$

$\displaystyle \frac{dy}{dx} = -\sin{x}\ln{3}^{\cos{x}}\ln{\ln{3}}$.