Published by:
CGP EDU Academic Team
Published on: September 12, 2026
If V = x 2 y + y 2 z then find 
(x, y, z)
Text Solution
Verified by ExpertsThe correct answer is:
A
Given the function V = x^2 y + y^2 z, we want to find the gradient \( \mathbf{E} = \nabla V \).
Step 1: Compute partial derivatives:
\( \frac{\partial V}{\partial x} = 2xy \)
\( \frac{\partial V}{\partial y} = x^2 + 2yz \)
\( \frac{\partial V}{\partial z} = y^2 \)
Step 2: Combine them into the gradient:
\( \mathbf{E} = \left(2xy, x^2 + 2yz, y^2\right)\)
Therefore, the required gradient is \( \nabla V = \left(2xy, x^2 + 2yz, y^2\right)\).
Step 1: Compute partial derivatives:
\( \frac{\partial V}{\partial x} = 2xy \)
\( \frac{\partial V}{\partial y} = x^2 + 2yz \)
\( \frac{\partial V}{\partial z} = y^2 \)
Step 2: Combine them into the gradient:
\( \mathbf{E} = \left(2xy, x^2 + 2yz, y^2\right)\)
Therefore, the required gradient is \( \nabla V = \left(2xy, x^2 + 2yz, y^2\right)\).
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