# Hello There. Needs help you guys to prove this simple partial derivatives for my research

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1. Oct 8, 2014

### iwan89

x^2 - y^2 +2mn +15 =0

x + 2xy - m^2 + n^2 -10 =0

The Question is:
Show that
del m/ del x = [m(1+2y) -2 x n ] / 2 (m^2 +n^2)

del m / del y = [x m+ n y] / (m^2 +n^2)

note that del= partial derivatives

My effort on solving this question is
Fx1=2x Fm1=2n
Fx2 =2y Fm2 =-2m

del m /del x = -Fx1/Fm1 + -Fx2/Fm2

the solution brings me nowhere near to answer..This is not a homework

Last edited: Oct 8, 2014
2. Oct 8, 2014

### Staff: Mentor

Could you use the advanced features and write your equations using latex?

Assuming I understand the first part of your post what does the fx1... stuff represent.

And what is the m and n are they variables dependent on x and y?

You mentioned this was for your research so what is the research and what level of math are you comfortable with?

3. Oct 8, 2014

### iwan89

@jedishrfu partial derivatives. Sorry sir im not really good in latex. I am very sorry and i was hoping that you can understand my question thank you.

4. Oct 8, 2014

### iwan89

i edited my question...

5. Oct 8, 2014

### Staff: Mentor

Okay but I still don't understand what Fx1/Fm1 is ?

Do you mean dx1/dm1 the derivative of x1 with respect to m1?

You really need to use latex so we can see the real equations.

6. Oct 8, 2014

### iwan89

@jedishrfu please ignore my solution.try to draft your own solution.. the real question is

x^2 - y^2 +2mn +15 =0

x + 2xy - m^2 + n^2 -10 =0

The Question is:
Show that
del m/ del x = [m(1+2y) -2 x n ] / 2 (m^2 +n^2)

del m / del y = [x m+ n y] / (m^2 +n^2)

note that del= partial derivatives

im doing fluid mechanics

7. Oct 8, 2014

### Staff: Mentor

Okay can you at least write your equations on paper and upload a photo of the paper?

The del notation confuses me as there is a del operator which when evaluated uses partial derivatives as in the gradient of some scalar function of x,y, z.

8. Oct 8, 2014

### Staff: Mentor

Looks like the current PF doesn't have an editor mode to latex and all The specialized math notation so I guess the photo route is the way to go.

9. Oct 8, 2014

### iwan89

this is the real question :) thanks!

10. Oct 9, 2014

### Staff: Mentor

x2 - y2 + 2uv + 15 = 0
x + 2xy - u2 + v2 - 10 = 0
Using LaTeX, show that:
$$\frac{\partial u}{\partial x} = \frac{u(1 + 2y) - 2xv}{2(u^2 + v^2)}$$
and
$$\frac{\partial u}{\partial y} = \frac{xu + vy}{u^2 + v^2}$$

You can right-click on the LaTeX stuff to show the Tex commands I used.

11. Oct 9, 2014

### Staff: Mentor

I haven't worked this all the way through, yet, but I would isolate the uv term in the first equation and take the partials of u with respect to x and then with respect to y. I would also isolate the u2 term in the second equation and take the partials of u w.r.t x and w.r.t. y.

Edit: I have worked this through for $\frac{\partial u}{\partial y}$ successfully, so the strategy I laid out above works. All it takes is a little bit of deft algebra to eliminate the partials of v with respect to the two independent variables.

Last edited: Oct 9, 2014
12. Oct 9, 2014

### iwan89

@Mark44 can you help me prove it? thank you so much :)

13. Oct 9, 2014

### Staff: Mentor

See post 11.

Last edited: Oct 9, 2014
14. Oct 9, 2014

### Staff: Mentor

Thanks guys.

15. Oct 9, 2014

### Ray Vickson

I think his question is now clear; he said exactly what his symbols represent. He said $\text{del} = \partial$.

However, we cannot help him until he demonstrates that he has done some work on the problem; he needs to show us his work. Those are the PF rules.

16. Oct 9, 2014

### Staff: Mentor

Yes, I agree. I was asking for a more precise definition from the OP before helping.

If you notice though the confusion I had was the use of m,n instead of u,v and the meaning behind the Fx1... In his posts. He mentioned it was for fluid mechanics which routinely use the del operator and I wanted to make sure things were right before guiding him to a solution.