Partial Derivatives MCQ Quiz in తెలుగు - Objective Question with Answer for Partial Derivatives - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

\(\rm \frac{\partial u}{\partial z} = xye^{xyz}\)

\(\rm \frac{\partial }{\partial y} \left( \rm \frac{\partial u}{\partial z} \right)= \rm \frac{\partial }{\partial y}(xye^{xyz})\)

\(\rm \frac{\partial^2 u}{\partial y \partial z} = xy \rm \frac{\partial }{\partial y}(e^{xyz}) + e^{xyz} \rm \frac{\partial }{\partial y}(xy)\)

= xy(xz)e^xyz + xe^xyz

\(\rm \frac{\partial }{\partial x} \left(\frac{\partial^2 u}{\partial y \partial z} \right) = \rm \frac{\partial }{\partial x}(x^2 yz + x) e^{xyz}\)

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (x^2 yz + x) yze^{xyz} + e^{xyz} (2xyz + 1)\)

\(\rm = e^{xyz} (x^2 y^2 z^2 + xyz + 2xyz + 1)\)

= (1 + 3xyz + x²y²z²) e^xyz

x, y, z = 1, 1, 1 रखने पर हमें प्राप्त होता है

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (1 + 3 + 1) e\)

= 5e

\(\rm \frac{\partial u}{\partial z} = xye^{xyz}\)

\(\rm \frac{\partial }{\partial y} \left( \rm \frac{\partial u}{\partial z} \right)= \rm \frac{\partial }{\partial y}(xye^{xyz})\)

\(\rm \frac{\partial^2 u}{\partial y \partial z} = xy \rm \frac{\partial }{\partial y}(e^{xyz}) + e^{xyz} \rm \frac{\partial }{\partial y}(xy)\)

= xy(xz)e^xyz + xe^xyz

\(\rm \frac{\partial }{\partial x} \left(\frac{\partial^2 u}{\partial y \partial z} \right) = \rm \frac{\partial }{\partial x}(x^2 yz + x) e^{xyz}\)

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (x^2 yz + x) yze^{xyz} + e^{xyz} (2xyz + 1)\)

\(\rm = e^{xyz} (x^2 y^2 z^2 + xyz + 2xyz + 1)\)

= (1 + 3xyz + x²y²z²) e^xyz

x, y, z = 1, 1, 1 रखने पर हमें प्राप्त होता है

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (1 + 3 + 1) e\)

= 5e