Question

Value of \(x \frac{∂u}{∂x}+y \frac{∂u}{∂y}\) if \(u=\frac{Sin^{-1} (\frac{y}{x})(\sqrt{x}+\sqrt{y})}{x^3+y^3}\) is?

(a) -2.5 u

(b) -1.5 u

(c) 0

(d) -0.5 u

This question was addressed to me in an interview for job.

The doubt is from Euler’s Theorem in portion Partial Differentiation of Engineering Mathematics

Answer 1

Correct choice is (a) -2.5 u

Best explanation: Since the function can be written as,

u=\(x^{\frac{-5}{2}} \frac{Sin^{-1} (\frac{y}{x})(1+\sqrt{\frac{y}{x}})}{1+(\frac{y}{x})^3}=x^n f(\frac{y}{x})\), by euler’s theorem,

\(x \frac{∂u}{∂x}+y \frac{∂u}{∂y} = -\frac{5}{2} u\)