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Math Help - Implicit Differentiation

  1. #1
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    Implicit Differentiation

    Hey guys im trying to learn implicit differentiation however I'm having some issues. Im trying to figure out when to use dy/dx or when to use yprime. Also im not sure which of the variables im supposed to use dy/dx with or yprime with.

    Heres a couple examples

    1. 2y - x / y^2 - 3 = 5

    2. x + y / 2x - y = 1

    I dont just need the answers I need to know why im using dy/dx or yprime and where to use each one correctly. Thanks so much guys.
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  2. #2
    MHF Contributor
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    dy/dx and y' are different notations for the same thing. The previous form is more explicit and tells us both the function name and the variable with which we are taking a derivative. y' is used as shorthand and implies the normal variable being used for the problem.

    For example if you have: x+y = 2y then the derivative of this equation with respect to x would be 1+dy/dx = 2dy/dx OR 1+y'=2y'. I like using the second way because it looks better and takes less time to write.
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