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Thread: implicit differentiation

  1. #1
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    implicit differentiation

    $\displaystyle

    3{^x}+log{_2}(xy)=10

    $
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  2. #2
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    Quote Originally Posted by simsima_1 View Post
    $\displaystyle

    3{^x}+log{_2}(xy)=10

    $
    The derivative of the right hand side with respect to x is zero.

    The derivative of the left hand side with respect to x requires differentiating $\displaystyle 3^x$ and $\displaystyle \log{_2} (xy)$ with respect to x.

    Note that:

    1. The derivative of $\displaystyle y = a^x$ with resepct to x is $\displaystyle (\ln a) \, a^x$

    2. The derivative of $\displaystyle y = \log_{a} x$ with resepct to x is $\displaystyle \left( \frac{1}{\ln a} \right) \, \frac{1}{x}$

    for appropriate values of a.

    Note also that you get the derivative of xy by using the product rule .....
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