Find the divergence of u=ex( y\, i+ y\, j).

GATE 2018 ME (ME2) – Question 12

Engineering Mathematics · Calculus: Gradient, divergence, curl, vector identities, line, surface and volume integrals · 1 mark · Multiple choice

Find the divergence of $\vec u=e^x(\cos y\,\hat i+\sin y\,\hat j)$.

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$e^x\cos y+e^x\sin y$
$2e^x\cos y$
$2e^x\sin y$

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Correct answer: (C) $2e^x\cos y$

Explanation

Divergence differentiates each component along its own coordinate: $$\nabla\cdot\vec u=\frac{\partial(e^x\cos y)}{\partial x}+\frac{\partial(e^x\sin y)}{\partial y}=2e^x\cos y.$$ Answer **C**.