- #1
Robin04
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Homework Statement
I have to calculate the partial derivative of an arctan function. I have started to calculate it but I wonder if there is any simpler form, because if the simplest solution is this complex then it would make my further calculation pretty painful...
Homework Equations
$$\beta = \arctan{(\frac{x^2 + y^2}{z^2})}$$
The Attempt at a Solution
$$\frac{\partial \beta}{\partial x} = \frac{\partial}{\partial x} (\arctan{(\frac{x^2 + y^2}{z^2})}) = \frac{1}{1+ (\frac{x^2 + y^2}{z^2})^2} \frac{\partial}{\partial x}(\frac{x^2 + y^2}{z^2}) = \frac{\frac{2x}{z^2}}{1+(\frac{x^2 + y^2}{z^2})^2} = \frac{2x}{z^2 + \frac{(x^2 + y^2)^2}{z^2}}$$
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