GATE 2021 CE (CE2) – Question 46

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 2 marks · Numerical answer

For $f(x,y)=xe^y$, find the directional derivative at (2,0) toward (1/2,2), as an integer.

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Correct answer: 1 to 1

Explanation

The direction vector is (−1.5,2), whose magnitude is 2.5, giving unit vector (−0.6,0.8). The gradient at (2,0) is $(e^0,2e^0)=(1,2)$. Their dot product is −0.6+1.6=**1**. Using the unnormalised direction would give the wrong derivative.