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Need hint on 'simple' differentiation problem

  1. Dec 1, 2004 #1
    I need to differentiate z = artan(y/x) with respect to x. Somehow z' = y/(1 +(1/x)^2) doesn't seem right.
     
  2. jcsd
  3. Dec 1, 2004 #2
    The derivative of arctan x = 1/(1 + x^2). There's a proof of that here.
     
  4. Dec 1, 2004 #3

    dextercioby

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    You know that
    [tex] [\arctan(f(x))]'=\frac{f'(x)}{1+f^2 (x)} [/tex]
    ,so apply the formula correctly.This is of course if "y" and "x" are independent variables.
     
  5. Dec 1, 2004 #4

    HallsofIvy

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    [tex] z'= \frac{1}{1+(\frac{y}{x})^2} \(-\frac{y}{x^2}\)[/tex]
    by the chain rule.

    Now multiply both numerator and denominator by x2.
     
  6. Dec 1, 2004 #5

    dextercioby

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    Apparently the sofware didn't read the paranthesis you've written,so it should be:
    [tex]z'= \frac{1}{1+(\frac{y}{x})^2} (-\frac{y}{x^2}) =-\frac{y}{x^2+y^2}[/tex]
     
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