Question

If z = x^n f(^y⁄x) then?

(a) y ^∂z⁄∂x + x ^∂z⁄∂y = nz

(b) 1/y  ^∂z⁄∂x + 1/x  ^∂z⁄∂y = nz

(c) x ^∂z⁄∂x + y ^∂z⁄∂y = nz

(d) 1/x  ^∂z⁄∂x + 1/y  ^∂z⁄∂y = nz

I have been asked this question by my college professor while I was bunking the class.

My doubt is from Euler’s Theorem topic in division Partial Differentiation of Engineering Mathematics

Answer 1

Right answer is (c) x ^∂z⁄∂x + y ^∂z⁄∂y = nz

To explain: Since the given function is homogeneous of order n, hence by euler’s theorem

x ^∂z⁄∂x + y ^∂z⁄∂y = nz.