यदि $u = x{y^2}{\tan ^{ - 1}}\left( {\frac{y}{x}} \right)$ है,तो $x{u_x} + y{u_y} = $

यदि $u = (x^2 + y^2 + z^2)^{3/2}$ है,तो $\left( \frac{\partial u}{\partial x} \right)^2 + \left( \frac{\partial u}{\partial y} \right)^2 + \left( \frac{\partial u}{\partial z} \right)^2 = $

यदि $u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right)$ है, तो $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ का मान क्या है?

यदि $u = \log ({x^2} + {y^2})$ है,तो $\frac{{\partial ^2}u}{\partial {x^2}} + \frac{{\partial ^2}u}{\partial {y^2}} = $

यदि $u=\sin ^{-1}\left(\frac{x^4+y^4}{x+y}\right)$ है,तो $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ का मान ज्ञात कीजिए।

यदि $u = e^{-x^2 - y^2}$ है,तो