Work Check On a Complicated Partial Derivative

[Liquid7800]

Homework Statement

Hello, I was given this complicated partial derivative to work out:

z = √( 1-( (x+y)/(xy) )² ) + arcsin (x+y)/(x-y)

find:

f_x and f_y

and this is my final answer taking the partial derivative with respect to 'x' only right now...which is rather nasty looking (sorry LaTex would not render out for me) :

z= -[ (x+y)/xy * (-x-y/x²y + 1/xy) ] / [ √( 1 - (x+y / xy)²) ] + [ -x-y/(x-y)² + 1/x+y ] / [ √( 1 - (x+y)² / (x-y)² ) ]

The complicated part (or peculiar) is that I really wanted to make sure my algebra etc. was correct. I tried using a CAS to check my work...but I noticed that depending how you entered the problem I got different answers ...
(somehow depends on if you enter the full problem in...or by how the denominator 'xy' is entered),
...so I didnt feel confident just using a CAS to check my work.

I would be very grateful if someone were to assist me.

Let me know if something is unclear... thanks again

 

[phyzguy]

I think you just have one sign error - your 1/(x+y) should be 1/(x-y). The whole thing should be
$$\frac{\frac{(x+y)^2}{x^3 y^2}-\frac{(x+y)}{x^2 y^2}}{\sqrt{1-\frac{(x+y)^2}{x^2 y^2}}}+\frac{\frac{1}{x-y}-\frac{x+y}{(x-y)^2}}{\sqrt{1-\frac {(x+y)^2}{(x-y)^2}}}$$

 

[Liquid7800]

Thanks very much for the reply, I hadnt simplified the whole thing yet...as I wanted to see if I was on the right track...and thanks for pointing that error out...that was a typo on my part.