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

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 ${x^x}{y^y}{z^z} = c$ है,तो ${{\partial z} \over {\partial x}} = $

यदि $f(x, y) = \frac{\cos(x - 4y)}{\cos(x + 4y)}$ है, तो $\left. \frac{\partial f}{\partial x} \right|_{y = \frac{x}{4}}$ का मान ज्ञात कीजिए:

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

यदि $u \equiv u(x, y) = \sin(y + ax) - (y + ax)^2$ है,तो यह क्या दर्शाता है?