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Thread: Differentiation

  1. #1
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    Differentiation

    Kindly help me with the following question.

    1. Consider the functional equation f(x-y)=f(x)/f(y). If f'(0)=p and f'(5)=q, then f'(-5) is
    A. p^2/q B. q/p C.p/q D. q

    I tried differentiating the function but then I would have dy/dx in the function which I do not know how to eliminate.
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  2. #2
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    Quote Originally Posted by champrock View Post
    Kindly help me with the following question.

    1. Consider the functional equation f(x-y)=f(x)/f(y). If f'(0)=p and f'(5)=q, then f'(-5) is
    A. p^2/q B. q/p C.p/q D. q

    I tried differentiating the function but then I would have dy/dx in the function which I do not know how to eliminate.
    In the equation f(x-y)=f(x)/f(y) there are two independent variables, x and y. It does not make sense to talk about dy/dx because x and y are independent of each other.

    What you need to do is to differentiate partially with respect to x and y. If you differentiate partially with respect to x then you find that f'(x-y) = \frac{f'(x)}{f(y)}. If you differentiate partially with respect to y then you find that -f'(x-y) = -\frac{f(x)}{(f(y))^2}f'(y). That gives you enough information to solve the problem.
    Last edited by Opalg; Mar 28th 2009 at 02:20 AM. Reason: fixed typo
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  3. #3
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    Thanks a lot!!
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