Problems On Differential Calculus I

Problems on Differential Calculus I:

7. Prove that

Solution: Since u = f (x,y) is a homogenous functions of degree n we have by the definition,

Thus we have proved the Euler's Theorem;

8. Prove that

Solution: Since u = f(x,y) is a homogenous function of degree n we have Euler's theorem

Differentiating (1) partially w.r.t x and w.r.t. y we get