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Math Help - Differential for func of the general form y = (a+b)^(1/z)

  1. #1
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    Differential for func of the general form y = (a+b)^(1/z)

    Hi,

    I was wondering if someone could enlighten me as to how I would find the partial differential for:
    <br />
q = \left(k^{\rho} + l^{\rho} \right)^{\frac{1}{\rho}}<br />

    trying to find:
    <br />
\frac{\partial q}{\partial l}, \mbox{whilst holding k const}<br />
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  2. #2
    MHF Contributor chisigma's Avatar
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    You can write...

    \displaystyle q= e^{\frac{\ln (k^{\rho} + l^{\rho})}{\rho} (1)

    ... and then remember that for an  q(l)= e^{\varphi(l)} is...

    \displaystyle \frac{d q}{dl} = e^{\varphi(l)}\ \frac{d \varphi (l)}{dl} (2)

    Kind regards

    \chi \sigma
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