maths partial derivatives question?

Question

Find the first partial derivatives for the following function, where they exist

s(x,y) = arctan(y/x)

thanks, any help much appreciated

Answer 1

When you take the partial derivative of a function with respect to some variable, you treat all other variables in that function as constant.

For example, y = 2x^2 + z^3

The partial of y with respect to x is 4x
The partial of y with respect to z is 3z^2

I'd start by getting your function in a different form using trig identities, until I had something easy to take the derivative of.

Answer 2

It would be of immense help to know the partial derivative with respect to which variable.
If you need the partial with respect to x, just take the derivative and treat y as if it was a constant. Likewise the partial with respect to y treats x as if it were a constant.

Doug

Answer 3

The partial with respect to y is x/(x^2+y^2) and the partial with respect to x is -y/(x^2+y^2).