# Math Help - derivative

1. ## derivative

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

2. Originally Posted by jojoferni244
what is the derivative of (ln(3))^cosx
recall that for any constant $a>0$, we have $\frac d{dx}a^x = a^x \ln a$

now, apply that rule with the chain rule to find this derivative.

the hard way is to use logarithmic differentiation

3. Originally Posted by jojoferni244
what is the derivative of (ln(3))^cosx
Let $u = \cos{x}$ so $y = \ln{3}^u$

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

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