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Math Help - arctan

  1. #1
    s7b
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    arctan

    How do you take the derivative of arctan(y/x) with respect to x??
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    Quote Originally Posted by s7b View Post
    How do you take the derivative of arctan(y/x) with respect to x??
    Why is this listed under "differential equations"?

    Are we to assume that y is not a function of x? Then use the chain rule, of course. The derivative of arctan(u), with respect to u, is \frac{1}{u^2+1}. By the chain rule, with u= y/x, the derivative of arctan(y/x), with respect to x, is \frac{1}{(y/x)^2+1}\frac{d(yx^{-1})}{dx}. Of course, you differentiate y/x= yx^{-1}, with respect to x, by treating y as a constant.
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    Quote Originally Posted by s7b View Post
    How do you take the derivative of arctan(y/x) with respect to x??
    To take the partial with respect to x, we treat y as a constant and since we have function composition we need the chain rule

    \frac{\partial }{\partial x}\tan^{-1}\left( \frac{y}{x}\right)=\frac{1}{1+\left( \frac{y}{x}\right)^2}\cdot \left( -\frac{y}{x^2}\right)=\frac{-y}{x^2+y^2}
    Last edited by TheEmptySet; March 27th 2009 at 11:46 AM. Reason: Ha ha I'm too slow
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