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Math Help - quick differentiating question

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    quick differentiating question

    how would I partially differentiate 1-x/(x^2+y^2) with respect to y and -y/(x^2+y^2) with respect to x.
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    Hello,
    Quote Originally Posted by anon18 View Post
    how would I partially differentiate 1-x/(x^2+y^2) with respect to y and -y/(x^2+y^2) with respect to x.
    1-\frac{x}{x^2+y^2}
    x is treated as a constant since you differentiate with respect to y.
    So \frac{\partial}{\partial y} \left(1-\frac{x}{x^2+y^2}\right)=-x \cdot \frac{\partial}{\partial y} \left(\frac{1}{x^2+y^2}\right)
    =x \cdot \frac{2y}{(x^2+y^2)^2} by applying the chain rule (the derivative of x^2+y^2 with respect to y is 2y)

    Same goes for the other one...
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