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Thread: Finding derivative dy/dx when y(x) is defined indirectly by an equation

  1. #1
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    Finding derivative dy/dx when y(x) is defined indirectly by an equation

    Hi,
    I feel embarrassed, but I forgot how to derive dY/dX when a function Y(X) is defined indirectly via an equation.
    For example, I have: X=Y*(Y+A)/B, where A and B are contstants. How do I find dY/dX?

  2. #2
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    Quote Originally Posted by Lzr0 View Post
    Hi,
    I feel embarrassed, but I forgot how to derive dY/dX when a function Y(X) is defined indirectly via an equation.
    For example, I have: X=Y*(Y+A)/B, where A and B are constants. How do I find dY/dX?
    That is called implicit differentiation. You would need to use chain rule and product rule (mostly).

    But for this problem (Quadratic equation), you can write:

    Y = [-A ± √(A2 + 4BX)]/2

    and carry-out straight-forward differentiation.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
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    Subhotosh, many thanks.
    Lazar

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