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Math Help - Need help differentiating an expression. Answer is given just unsure of the steps.

  1. #1
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    Need help differentiating an expression. Answer is given just unsure of the steps.

    Hello, this problem states to differentiate the expression with respect to q. I am not sure of the steps taken to get the final result.

    This is an economics problem differentiating the variable cost function to get the marginal cost function.
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  2. #2
    Super Member Quacky's Avatar
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    Re: Need help differentiating an expression. Answer is given just unsure of the steps

    So you want to differentiate:

    6(\frac{q}{10k^{0.4}})^{1.67} with respect to q?

    In which case, we have:

    6\frac{q^{1.67}}{(10k^{0.4})^{1.67}}

    = \frac{6q^{1.67}}{(10k^{0.4})^{1.67}}

    But the \frac{6}{(10k^{0.4})^{1.67}}(everything except the q^{1.67}) is just constant. It's a stable value, like 4 or 7 - it isn't a variable.

    For the sake of simplicity, I'm going to let \frac{6}{(10k^{0.4})^{1.67}}=c

    When we differentiate 4x^n with respect to x, we get: 4nx^{n-1}.

    When we differentiate ax^n with respect to x, we get: anx^{n-1}

    We have: c\times~q^{1.67}

    So, differentiating, we get: 1.67c\times~q^{0.67}

    Then, slipping c back in as \frac{6}{(10k^{0.4})^{1.67}}, we have:

    \frac{1.67\times~6\times~q^{0.67}}{(10k^{0.4})^{1.  67}}

    and 1.67\times~6=10.02 which is where that number arises.
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