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Implicit differentiation

  1. Jul 20, 2007 #1
    1. The problem statement, all variables and given/known data
    I just got started on this, and am not grasping the WHOLE idea.
    1.xy=25 The answer says -y/x
    2.x^2+3xy+y^2=15 And this says -y^2/x^2

    2. Relevant equations
    1. dy/dx(xy)= dy/dx(25)
    1=0 ???
    2.dy/dx x^2+3xy+y^2= dy/dx 15
    2x+3+y(dy/dx) =0
    3. The attempt at a solution
    2. -2x-3/y (which i know is not right.)
  2. jcsd
  3. Jul 20, 2007 #2


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    The basic idea is this: Consider y as a function of x.

    For example, you have x times y(x) = 25.

    Now differentiate both sides with respect to x. You may use the chain rule on the product x times y(x).

    [tex] \frac{d}{dx} ( x y(x)) = \frac{d}{dx} (25) [/tex]

    Apply the chain rule, take the derivatives and then isolate dy/dx.
  4. Jul 20, 2007 #3
    I don't know if I got this right.
    I used the product rule: (x)(y(x))'+(x)'(y(x)) and for derivitive of y(x), I used the
    chain rule to find the derivitive. And got(x)(1*x*x)+(x)(y(x)). -> x^3+xy(x)d/dx=0 What else am I doing wrong?
  5. Jul 20, 2007 #4


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    You can't use the chain rule to find the derivative of y(x) since it's an unknown function. Just leave it as [itex] y' [/itex]! Now, using (x)' = 1, you get

    y + x y' = 0 so y' = -y/x

    It's that simple!
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