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Math Help - implicit differentiation

  1. #1
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    implicit differentiation

    <br /> <br />
3{^x}+log{_2}(xy)=10<br /> <br />
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  2. #2
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    Quote Originally Posted by simsima_1 View Post
    <br /> <br />
3{^x}+log{_2}(xy)=10<br /> <br />
    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 3^x and \log{_2} (xy) with respect to x.

    Note that:

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

    2. The derivative of y = \log_{a} x with resepct to x is \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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