A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 4 years ago

Here's one: find the derivative of (xy)^x = e Thanks!

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

    This is what I did: I took the natural log to both sides xln(xy)=1 I divided x out of each side ln(xy)=1/x Used properties of logarithms to separate out ln(xy) lnx + lny=1/x lny=-lnx+1/x then I took the derivative to both sides y'/y=-[(1/x^2)+(1/x)] I then multiplied both sides by y, which I just found by using the earlier equation: lny=-lnx+1/x y=e^(-lnx+1/x) y'=-[(1/x^2)+(1/x)][e^(-lnx+1/x)] But I'm sure there's an easier or different way, I just went about it this route since this is where I felt most comfortable.

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Very interesting. I asked the question somewhere else and got a different approach but same response. This is actually very helpful to see it done a couple different ways. And thanks for the extra explanations!

  3. 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.