1. Not finding help here? Sign up for a free 30min 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!

Find the derivative (Implicit)

  1. Jun 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Find [tex]\frac{\partial\theta}{\partial y}[/tex]

    [tex]z=rcos\theta[/tex]
    [tex]x=rsin\theta\cos\phi[/tex]
    [tex]y=rsin\theta\sin\phi[/tex]
    [tex]r^2=x^2 + y^2 + z^2[/tex]


    3. The attempt at a solution

    We know [tex]cos\theta=\frac{z}{r}=\frac{z}{\sqrt{x^2 + y^2 + z^2}}[/tex]

    So implicit differentiation says to differentiate both sides with respect to y and this is where I begin to run into trouble.

    Please be very specific when you try to explain how this is done lol.

    Thanks!
     
  2. jcsd
  3. Jun 1, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    Do you know how to do implicit differentiation? Do you know how find the partial derivative of a function with respect to a variable?
     
  4. Jun 1, 2009 #3
    An earlier part to this question was to find [tex]\frac{\partial r}{\partial y}[/tex] and I solved it correctly.

    Here is how I did it.

    [tex]r^2= x^2 + y^2 + z^2[/tex]

    [tex]\frac{d}{dy}r^2= \frac{d}{dy}y^2[/tex]

    [tex]\frac{d}{dr}r^2\frac{dr}{dy}=2y[/tex]

    [tex]2r\frac{dr}{dy}=2y[/tex]

    so therefore [tex]\frac{\partial r}{\partial y}= \frac{y}{r}[/tex]

    I am just having some difficulty with the next part of the question.
     
  5. Jun 1, 2009 #4
    In more specific terms, differentiate both sides of the equation with respect to y keeping all variables other than y and those that are explicit functions of y constant.
    Where specifically did you run into trouble?
     
  6. Jun 1, 2009 #5
    The Right Hand Side of the equation gives me the difficulty. I am sure I am making an elementary mistake.

    [tex]\frac{\partial\theta}{\partial y}:[/tex]

    [tex]\frac{d}{dy}cos\theta=\frac{d}{dy}(\frac{z}{r})[/tex]

    [tex]\frac{d}{d\theta}(cos\theta)\frac{d\theta}{dy}=\frac{d}{dr}r^-1\frac{dr}{dy}[/tex]

    [tex]-sin\theta\frac{d\theta}{dy}=-r^-2\frac{dr}{dy}[/tex]

    I have a feeling that I have already made a mistake with the right side...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find the derivative (Implicit)
  1. Implicit derivation (Replies: 2)

  2. Implicit Derivation (Replies: 10)

  3. Implicit Derivation (Replies: 9)

Loading...