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!

Quick derivative question

  1. Jan 10, 2004 #1
    How do you find the derivative of y=x^y ?
     
  2. jcsd
  3. Jan 10, 2004 #2
    [tex]\begin{align*}
    y&=x^y \\
    \ln y&=y\ln x \\
    \frac{y^\prime}{y}&=y^\prime\ln x+\frac{y}{x} \\
    y^\prime\left(\frac{1}{y}-\ln x\right)&=\frac{y}{x} \\
    y^\prime&=\frac{y^2}{x-xy\ln x}
    \end{align*}[/tex]
     
  4. Jan 10, 2004 #3
    Not quite the answer I was looking for, but thanks any how. I already know how the problem is solved.
     
  5. Jan 10, 2004 #4
    You asked me how to find the derivative. I showed you a way to do it. What were you looking for?
     
  6. Jan 11, 2004 #5
    I was looking for something more like this: x'=y^(1/y)*(1/y^2-ln(y)/y^2).

    I solved it though, guess just got stuck for a minute.
     
  7. Jan 11, 2004 #6
    Usually people want the derivative of y wrt x. Plus, you gave an equation for y in terms of x and y.
     
  8. Jan 11, 2004 #7
    Since y does not equal f(x), y can not be expressed in terms of x. We would have to express x in terms of y.

    Of course, it would be much better if the equation was x=y^x, then it can be expressed as y=x^(1/x).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quick derivative question
  1. Quick question (Replies: 1)

  2. Quick Question (Replies: 2)

  3. Quick question (Replies: 3)

  4. Quick Question (Replies: 2)

  5. A quick question. (Replies: 4)

Loading...