• Support PF! Buy your school textbooks, materials and every day products Here!

Partial Derivative of atan(xy/(1+x^2+y^2)^0.5)

  • #1
160
3

Homework Statement



Prove that if ##z=\arctan(\frac{xy}{\sqrt(1+x^2+y^2)})## , then:

##\frac{\partial^2 z}{\partial x \partial y}=\frac{1}{(1+x^2+y^2)^\frac{3}{2}} ##

Homework Equations



##\frac{d}{d x} (\arctan(x)) = \frac{1}{1+x^2}##

The Attempt at a Solution



Differentiating z partially w.r.t y, I got:

## \frac{\partial z}{\partial y} = \frac{x^3+x}{(1+x^2+y^2)^\frac{3}{2} (1+x^2+y^2+x^2y^2)} ##

I'm pretty sure my working till here is correct. But differentiating again w.r.t x would be disastrous. Help me please. :)
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
Hi MrWarlock616! :smile:

You can cancel a (1 + x2), top-and-bottom :wink:
 
  • #3
160
3
EDIT: -nvm got it-
 

Related Threads on Partial Derivative of atan(xy/(1+x^2+y^2)^0.5)

  • Last Post
Replies
4
Views
850
Replies
1
Views
7K
Replies
3
Views
1K
Replies
2
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
12
Views
10K
  • Last Post
Replies
1
Views
9K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
8
Views
2K
Top