Hi All,

To be able to construct a Jacobian, I am asked to find the two partial derivatives of the following inverse trigonometric function:

$\displaystyle w_{1}(u,v) = \frac{1}{2\pi} \arccos (\frac{u}{\sqrt{u^{2} + v^{2}}})$

I know that $\displaystyle \frac{\delta \arccos x}{\delta x} = \frac{-1}{\sqrt{1-x^2}}$, but I am realy stumped at how to proceed from this to get the partial derivatives.

The anwers to the partian derivatives are given as:

$\displaystyle \frac{\delta w_{1}}{\delta u} = \frac{-v}{2\pi(u^{2}+v^{2})}$

$\displaystyle \frac{\delta w_{1}}{\delta v} = \frac{u}{2\pi(u^{2}+v^{2})}$

Any help on how to arrive here would be much appreciated!

Kind regards,

Chris