Find the divergence of F=x2y i+y3x j at (3,2).

GATE 2026 MN – Question 12

Engineering Mathematics · Vector Calculus · 1 mark · Multiple choice

Find the divergence of $\mathbf F=x^2y\mathbf i+y^3x\mathbf j$ at (3,2).

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Correct answer: (D) 48

Explanation

Differentiate each component with respect to its corresponding coordinate: ∇·F=2xy+3xy². At x=3,y=2, the two terms are12 and36, giving48. Therefore D; cross derivatives are not used in divergence.

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