Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problems with implicit differentiation

  1. May 10, 2007 #1
    In a problem where I need to use implicit diff. to find the slope of a line such as:

    y^2 + x^2 = 9

    2y (dy/dx) + 2x = 0

    dy/dx = -y/x

    Where does the (dy/dx) after the 2y (in the second part) come from? I've already differentiated y^2, x^2, and 9. Why isn't it just 2y + 2x = 0? I've looked all over, and in every problem an extra (dy/dx) or two just seem to pop up out of nowhere. Thanks!
  2. jcsd
  3. May 10, 2007 #2
    Think of Y as a function in X. Then it's just the chain rule.

    For example if y=e^x+x^3
    y' = e^x + 3x^2

    y^2 + x^2 = 9 is

    (e^x+x^3)^2 + x^2 - 9 = 0
    when we plug in y

    differentiating this we get
    2(e^x+x^3)(e^x + 3x^2) + 2x = 0

    or 2y*(dy/dx) +2x = 0

    when you do implicit differentiation you are doing it for a general y function of x instead of something specific (like as in our case of y=e^x+x^3)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook