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Math Help - Problem: Let Y = cosx + sinx / cosx - sinx. Find dy/dc

  1. #1
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    Problem: Let Y = cosx + sinx / cosx - sinx. Find dy/dc

    Having trouble finding the answer to this question:

    Let Y = cosx + sinx / cosx - sinx

    Find dy/dx

    The answer is supposed to be (cosx - sinx)(-sinx + cosx)-(cosx + sinx)(-sinx - sinx) / (cosx-sinx)^2 which can be simplified further

    But I have no idea how this is gotten Please Help!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Problem: Let Y = cosx + sinx / cosx - sinx. Find dy/dc

    You have a minor typo in your intended result, but it is obtained by using the quotient rule:

    \frac{d}{dx}\left(\frac{f(x)}{g(x)} \right)=\frac{f'(x)g(x)-f(x)g'(x)}{g^2(x)}

    For the function you cite, we also need:

    \frac{d}{dx}(\sin(x))=\cos(x)

    \frac{d}{dx}(\cos(x))=-\sin(x)
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    Re: Problem: Let Y = cosx + sinx / cosx - sinx. Find dy/dc

    I got  y' = \frac{(-sinx+cosx)(cosx-sinx)-(cosx+sinx)(-sinx-cosx)}{(cosx-sinx)^2}

    Remember that the numerator and denominators are quantities, and you need to take the derivative of the top and bottom quantities in accordance with the quotient rule.
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  4. #4
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    Re: Problem: Let Y = cosx + sinx / cosx - sinx. Find dy/dc

    Quotient rule! Thank you!
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