Question

verify euler's theorem for the function u= axy+byz+ezx​

Answer 1

Answer:

Step-by-step explanation:

f(x, y, z) = axy + byz + czx - - - (1)

Taking derivative of (1) with respect to x.

df/dx = ay + cz

Multiplying by x we get,

x.df/dx = axy + czx - - - (2)

Taking derivative of (1) with respect to y.

df/dy = ax + bz

Multiplying by y we get,

y.df/dy = axy + byz - - - (3)

Taking derivative of (1) with respect to z.

df/dz = by + cz

Multiplying by z we get,

z.df/dz = czx + byz - - - (4)

Adding (2) , (3), (4)

x.df/dx + y.df/dy + z.df/dz = 2 (axy + byz + czx)

x.df/dx + y.df/dy + z.df/dz = 2 f(x, y, z) -- Euler’s Theorem verified