A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 5 years ago

show that the relation (x^3 + y^3 = 6xy) implicitly defines a solution to (dy/dx)=(2y-x^2)/((y^2)-2x)

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Use implicit differentiation, plus product rule and chain rule as you know them. The only difference is that y is a function of x, f(x), so when you take the derivative of y, you must multiply the result by dy/dx. This is just an application of chain rule, but it's a little complicated to explain and time is short. Taking your equation, the derivative of x^3 is just 3x^2, as usual. The derivative of y^3, however, is 3y^2 times dy/dx, by chain rule, as I said above. On the right side, hide the constant (6), then use product rule to take the derivative. Again, any time you take a derivative of y, multiply by dy/dx. Take derivatives of x normally. Okay, now you have a new equation with a couple of dy/dx's in it. Just like solving simple equations, gather all the terms containing dy/dx onto one side, and all the non-dy/dx terms on the other. Factor out dy/dx, then divide to isolate dy/dx. There. You've got dy/dx.

  2. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.