Question

If u=x2y+y2z+z2x then show that du/dx + du/dy + du/dz = (x+y+z)2​

Answer 1

Answer:

du/dx=2x,,du/Dy=2y,,do/dz=2z

at x=y=z=1

2(1)+2(1)+2(1)=6

Answer 2

du/dx +du/dy + du/dz = (x+y+z)²

Given: u=x2y+y2z+z2x

To Prove: du/dx +du/dy + du/dz = (x+y+z)²

Solution:

u= x2y+y2z+z2x

du/dx = 2xy  + z²

du/dy = x² +2yz

du/dz = y² + 2zx

Now, du/dx +du/dy + du/dz = 2xy  + z² +  x² +2yz + y² + 2zx

du/dx +du/dy + du/dz = (x+y+z)²

Hence, Proved by the given explanation.

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