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    derivative

    what is the derivative of (ln(3))^cosx
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    Quote Originally Posted by jojoferni244 View Post
    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
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    Quote Originally Posted by jojoferni244 View Post
    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}}.
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