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Math Help - Derivative of arctan(x/y)

  1. #1
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    Derivative of arctan(x/y)

    Trying to figure out the derivative of arctan(x/y)

    Thank you Very much

    ViperRobK
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  2. #2
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    Quote Originally Posted by ViperRobK View Post
    Trying to figure out the derivative of arctan(x/y)

    Thank you Very much

    ViperRobK
    You don't. At least not until you have clarified the problem. Is this a function of the two independent variables x and y, and you want the two partial derivatives or is one of the variables and function of the other (and if so, what function)?
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  3. #3
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    it is a function of 2 independent variable and derivative with respect to x sorry for the lack of detail
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  4. #4
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    Think i figured it out if someone could confirm

    \frac{y-\frac{dy}{dx}}{y^2+x^2}
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  5. #5
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    if we take the partial derivative with respect to x, we would get:

    \frac{\partial}{\partial x} \arctan \left( \frac{x}{y} \right)

    =\frac{1}{1+(x/y)^2} \times \frac{1}{y} = \frac{1}{y+x^2/y} = \frac{y}{y^2+x^2} so your solution is correct.
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