Can this be done in an easier way?

This question has been posed in multiple posts due to the many attachements

Hi there!


For one of my exercises I have the following equation:

CodeCogsEqn (9).gif

I need to find both partial derivatives and for y this is quite easy.

However I find that finding the partial derivative of x is very time-consuming.

I was hoping that someone could show me whether there is an easier way of computing this.

Here is what I did.

Rewrite abs[x] to sqrt(x ²) and apply quotient rule

CodeCogsEqn (2).gif

Note that x ²+y ² in the denominator should be (x ²+y ²) ² also I accidently used the wrong notation for the derivative

Apply product rule

CodeCogsEqn (3).gif

Note that in the first part of the equation x ²+y ² in the denominator should be (x ²+y ²) ²

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