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GATE 2019 ME (ME2) – Question 12

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

Find the directional derivative of $f(x,y)=x^2+y^2$ along the line directed from (0,0) to (1,1), evaluated at x = 1, y = 1.

  1. $\sqrt2$
  2. 2
  3. $2\sqrt2$
  4. $4\sqrt2$

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Correct answer: (C) $2\sqrt2$

Explanation

The gradient is $(2x,2y)$,giving(2,2) at the point. Normalize the direction to $(1,1)/\sqrt2$. Their dot product is $4/\sqrt2=\mathbf{2\sqrt2}$,optionC. A direction vector must be normalized before taking the directional derivative.