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  • Oct 18, 2007, 12:31 PM
    jd2007
    Calculus (Implicit Differentiation)
    I need to find (dy/dx) for this problem "x^(1/2)+y^(1/2)=1" in two ways:

    a) implicit differentiation, and
    b) differentiating an explicit formula for y.



    Thank you!
  • Oct 18, 2007, 01:23 PM
    ebaines
    First, to do the explicit diffentiation, rearrange the equation in the form y = f(x), and differentiate as normal. You should end up with dy/dx =f'(x), meaning it's a function of x only.

    For implicit diffentiation, you set up the equation in the form F(x,y) = 0. In this case you have:

    sqrt(x) + sqrt(y) -1 =0.
    Differentiate with respect to x, and you get



    which can be rearranged to give the answer as a function of both x and y.

    Here's a site that works through a few problems that may be of help:

    Visual Calculus - Implicit Differentiation

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