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Homework Help: 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]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.

  2. jcsd
  3. Jun 1, 2009 #2


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    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]



    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]




    I have a feeling that I have already made a mistake with the right side...
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