Partial Derivative with Respect to y of a*cos(xy)-y*sin(xy)

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Homework Statement


Find the partial derivative of a*cos(xy)-y*sin(xy) with respect to y.

Homework Equations


None.

The Attempt at a Solution


The answer is -ax*sin(xy)-sin(xy)-xy*cos(xy).
I know that I need to treat x as constant since I need to take the partial derivative with respect to y. But I don't know how to get -sin(xy). I know how to get -ax*sin(xy) and -xy*cos(xy).
 
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Never mind. I got it.
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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