1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Implicit Differentiation to find dy/dx

  1. Oct 10, 2013 #1
    Use implicit differentiation to find dy/dx given x^2y+xy^2=4.

    I have no idea how to approach this problem. My instructor assigned this as homework but has not gone over it at all in class. We have gone over explicit differentiation and I understand this well. I have read the section but it is making no sense. I think I need to use the General Power Rule: d/dx(y^n)=ny^(n-1)dy/dx but I don't know how to use it.
  2. jcsd
  3. Oct 10, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    You've got all the ingredients. Differentiate both sides with respect to x and solve for dy/dx. Use the product rule on the way.
  4. Oct 10, 2013 #3
    Can you explain a little more. I don't understand "with respect to x or y." How do I use the general power rule?
  5. Oct 10, 2013 #4


    User Avatar
    Science Advisor

    You said, with reference to implicit differentiation, "I understand this well". Did you mean to say "I don't understand this well"?

    Differentiating "with respect to x" means treating y as a function of x, not a separate variable. So "[itex]y^n[/itex], differentiated "with respect to y" would be just [itex]d(y^n)/dy= ny^{n-1}[/itex]. But differentiating "with respect to x" you would use the chain rule: [tex]d(y^n)/dx= ny^{n-1} (dy/dx)[/tex].

    If you had, for example, [itex]x^2y+ xy^2= x- y[/itex], differentiating each part with respect to x, (using the "product rule" for the terms on the left), [itex]2xy+ x^2(dy/dx)+ (1)y^2+ 2xy(dy/dx)= 1- dy/dx[/itex]. You can then solve that equation for dy/dx.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted