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if u=f(x/y,y/z,z/x) then show that xdu/dx+ydu/dy+zdu/dz

if u=f(x/y,y/z,z/x) then show that xdu/dx+ydu/dy+zdu/dz

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Grade:12th pass

1 Answers

Shraddha Singh
49 Points
one month ago
 
u=f(r,s,t)
 and r=x/y, s=y/x, t=z/x
 
du/dx= du/dr*dr/dx+du/ds*ds/dy+du/dt*dt/dx
 
du/dx=f'(u)(1/y)+0+f'(u)(-z/x²)
 
xdu/dx=f'(u)(x/y)+f'(u)(-z/x)
 
Similarly
 
ydu/dy=f'(u)(-x/y)+f'(u)(y/z)  
and
xdu/dz=f'(u)(-y/z)+f'(u)(z/x)
 
Now
xdu/dx+ydu/dy+xdu/dz
 
Putting the value
=0

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