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Math Help - implicit differentiation of an exponential function in two variables

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    implicit differentiation of an exponential function in two variables

    implicit differentiation of an exponential function in two variables-screen-shot-2012-10-24-2.06.48-am.png


    for the RHS how would I tackle this?

    I know for taking the derivative of a^x would give a^x*ln(a) but im not sure how to apply that in this situation, given that one of the exponential variables (y) is itself a function of x.
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    MHF Contributor FernandoRevilla's Avatar
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    Re: implicit differentiation of an exponential function in two variables

    Quote Originally Posted by kingsolomonsgrave View Post
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    2^{xy}(y+xy')\ln 2=y'+1
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    Re: implicit differentiation of an exponential function in two variables

    thanks!

    how would I solve for y' in this case? Just multipy by 2^xy, group like terms and solve as normal?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: implicit differentiation of an exponential function in two variables

    Quote Originally Posted by kingsolomonsgrave View Post
    how would I solve for y' in this case? Just multipy by 2^xy, group like terms and solve as normal?
    Solve it as a first degree equation on the unknown y'. You'll obtain y'=\dfrac{y2^{xy}}{1-x2^{xy}\ln 2} .
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