Partial Derivatives MCQ Quiz in తెలుగు - Objective Question with Answer for Partial Derivatives - ముఫ్త్ [PDF] డౌన్లోడ్ కరెన్
Last updated on Apr 7, 2025
Latest Partial Derivatives MCQ Objective Questions
Partial Derivatives Question 1:
यदि u = exyz, तब \(\rm \frac{\partial^3 u}{\partial x \partial y \partial z}\) पर (1, 1, 1) _____ है।
Answer (Detailed Solution Below)
Partial Derivatives Question 1 Detailed Solution
\(\rm \frac{\partial u}{\partial z} = xye^{xyz}\)
\(\rm \frac{\partial }{\partial y} \left( \rm \frac{\partial u}{\partial z} \right)= \rm \frac{\partial }{\partial y}(xye^{xyz})\)
\(\rm \frac{\partial^2 u}{\partial y \partial z} = xy \rm \frac{\partial }{\partial y}(e^{xyz}) + e^{xyz} \rm \frac{\partial }{\partial y}(xy)\)
= xy(xz)exyz + xexyz
\(\rm \frac{\partial }{\partial x} \left(\frac{\partial^2 u}{\partial y \partial z} \right) = \rm \frac{\partial }{\partial x}(x^2 yz + x) e^{xyz}\)
\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (x^2 yz + x) yze^{xyz} + e^{xyz} (2xyz + 1)\)
\(\rm = e^{xyz} (x^2 y^2 z^2 + xyz + 2xyz + 1)\)
= (1 + 3xyz + x2y2z2) exyz
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
Top Partial Derivatives MCQ Objective Questions
Partial Derivatives Question 2:
यदि u = exyz, तब \(\rm \frac{\partial^3 u}{\partial x \partial y \partial z}\) पर (1, 1, 1) _____ है।
Answer (Detailed Solution Below)
Partial Derivatives Question 2 Detailed Solution
\(\rm \frac{\partial u}{\partial z} = xye^{xyz}\)
\(\rm \frac{\partial }{\partial y} \left( \rm \frac{\partial u}{\partial z} \right)= \rm \frac{\partial }{\partial y}(xye^{xyz})\)
\(\rm \frac{\partial^2 u}{\partial y \partial z} = xy \rm \frac{\partial }{\partial y}(e^{xyz}) + e^{xyz} \rm \frac{\partial }{\partial y}(xy)\)
= xy(xz)exyz + xexyz
\(\rm \frac{\partial }{\partial x} \left(\frac{\partial^2 u}{\partial y \partial z} \right) = \rm \frac{\partial }{\partial x}(x^2 yz + x) e^{xyz}\)
\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (x^2 yz + x) yze^{xyz} + e^{xyz} (2xyz + 1)\)
\(\rm = e^{xyz} (x^2 y^2 z^2 + xyz + 2xyz + 1)\)
= (1 + 3xyz + x2y2z2) exyz
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