Home › Previous year questions › GATE 2020 MT › Question 39GATE 2020 MT – Question 39 Engineering Mathematics · Calculus and vector calculus · 2 marks · Multiple choice
Find the divergence of $(x^3+y^3)\mathbf i+3xy^2\mathbf j+3zy^2\mathbf k$.
$3y^2+6xy+6x^2$ $3x^2+6y^2+9xy+6yz$ $12xyz$ $3(x+y)^2$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (D) $3(x+y)^2$
Explanation Differentiate the x-component with respect to x, y-component with respect to y, and z-component with respect to z. Their sum is $3x^2+6xy+3y^2=3(x+y)^2$, D. Cross derivatives belong to different vector-calculus operations and do not enter divergence.
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