Question

What is the derivative of `arctan(y/x)`?

Answer 1

`- y/(x^2 + y^2) dy/dx`

Explanation:

`d/(dx) arctan(y/x) = 1/(1 + (y/x)^2) * (d/dx y/x)`
`d/(dx) arctan(y/x) = 1/(1 + (y^2/x^2)) * (- y/x^2 * dy/dx)`
`d/(dx) arctan(y/x) = - x^2/(x^2 + y^2) * y/x^2 * dy/dx`
`d/(dx) arctan(y/x) = - y/(x^2 + y^2) dy/dx`