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 posed to me during an online interview.

The question is from Partial Differentiation topic in chapter Partial Differentiation of Engineering Mathematics

Answer 1

Right option is (a) -2.5 u

To explain: 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 equler’s theorem,

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