Discussion
The gradient of \( V = x^2 y \) is
Answer: C
Correct answer: \( 2xy\,\mathbf{a}_x + x^2\mathbf{a}_y \)
Each component of the gradient is the partial derivative with respect to that coordinate: \( \partial V/\partial x = 2xy \), \( \partial V/\partial y = x^2 \), and \( \partial V/\partial z = 0 \). Note that y is held constant while differentiating with respect to x, which is what leaves the y in the first component.
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