# Derivative of arctan(x/y)

• Jan 15th 2009, 11:19 AM
ViperRobK
Derivative of arctan(x/y)
Trying to figure out the derivative of arctan(x/y)

Thank you Very much

ViperRobK
• Jan 15th 2009, 11:23 AM
HallsofIvy
Quote:

Originally Posted by ViperRobK
Trying to figure out the derivative of arctan(x/y)

Thank you Very much

ViperRobK

You don't. At least not until you have clarified the problem. Is this a function of the two independent variables x and y, and you want the two partial derivatives or is one of the variables and function of the other (and if so, what function)?
• Jan 15th 2009, 11:35 AM
ViperRobK
it is a function of 2 independent variable and derivative with respect to x sorry for the lack of detail
• Jan 15th 2009, 02:47 PM
ViperRobK
Think i figured it out if someone could confirm

$\displaystyle \frac{y-\frac{dy}{dx}}{y^2+x^2}$
• Jan 15th 2009, 03:27 PM
lllll
if we take the partial derivative with respect to x, we would get:

$\displaystyle \frac{\partial}{\partial x} \arctan \left( \frac{x}{y} \right)$

$\displaystyle =\frac{1}{1+(x/y)^2} \times \frac{1}{y} = \frac{1}{y+x^2/y} = \frac{y}{y^2+x^2}$ so your solution is correct.