How do u, v, and w relate to the derivatives of x and y?

kidia
Messages
65
Reaction score
0
I need a help on this question,Show that if u=x-y,v=xy and w=f(u,v) then x\frac{dw}{dx}-y\frac{dw}{dy}=(x-y)\frac{dw}{du}.
 
Physics news on Phys.org
To simplify writing, I will use d for partial derivatives.

f(u,v)=f(x-y,xy)
df/dx=df/du+ydf/dv
df/dy=-df/du+xdf/dv
xdf/dx-ydf/dy=(x+y)df/du

Note difference! (x+y) not (x-y)
 
Suggest moving this to Calc homework pages.

~H
 
Done! xxxxxxxxx
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top