જો $u(x, y)=y \log x+x \log y$ હોય,તો $u_x u_y-u_x \log x-u_y \log y+\log x \log y$ ની કિંમત શું 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}} = $

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

જો $z = \sec^{-1}\left(\frac{x^4+y^4-8x^2y^2}{x^2+y^2}\right)$ હોય,તો $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ ની કિંમત શોધો.

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 $z = \frac{(x^4 + y^4)^{1/3}}{(x^3 + y^3)^{1/4}}$ હોય,તો $x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y} = $