Question

If $Z^2=\frac{x^{1/2}+y^{1/2}}{x^{1/3}+y^{1/3}}$

then $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=?$

• A. $\frac{z}{6}$
• B. $\frac{z}{3}$
• C. $\frac{z}{2}$
• D. $\frac{z}{12}$

Answer 1

The correct option is D $\frac{z}{12}$

$Z={\left(\frac{x^{1/2}+y^{1/2}}{y^{1/3}+x^{1/3}}\right)}^{\frac{1}{2}}$

So Z is of degree $n=\frac{1}{12}$

$\sum x\frac{\partial z}{\partial x}=nz$

$=\frac{1}{12}z$