Consider $u(x, y).$ Let $v = \frac{\partial u}{\partial x}.$ Now let $w(x) = u(x, 0).$ My question is, is $v(x, 0) = \frac{d w}{d x}?$ I have a feeling this is true but I'm not quite sure...
2026-03-30 17:54:43.1774893283
Is taking the partial with one variable held constant the same as the derivative of that function?
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