1. ## 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.

2. Hello,
Originally Posted by anon18
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...