જો $u = \log_e(x^2 + y^2) + \tan^{-1}\left(\frac{y}{x}\right)$ હોય,તો $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = $

જો $u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right)$ હોય, તો $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ નું મૂલ્ય શું થાય?

જો $u = \frac{x + y}{x - y}$ હોય,તો $\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} = $

$\begin{aligned} & f(x, y)=2(x-y)^2-x^4-y^4 \\ & \left|\left(f_{x x} f_{y y}-f_{x y}^2\right)\right|_{(0,0)} \end{aligned}$

જો $z = \frac{y}{x} \left[ \sin \frac{x}{y} + \cos \left( 1 + \frac{y}{x} \right) \right]$ હોય, તો $x \frac{\partial z}{\partial x}$ કોના બરાબર થાય?

જો ${z^2} = \frac{{x^{1/2} + y^{1/2}}}{{x^{1/3} + y^{1/3}}}$ હોય,તો $x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = $