GATE EE 2025 Set 1 — Question 53
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Engineering Mathematics → Vector Calculus → Directional Derivatives
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Question
Let . The rate of change of the real valued function,at the origin in the direction of the point is ___________ (round off to the nearest integer).
Correct answer
0 to 1
Solution
The rate of change of at a point in a given direction is the directional derivative.Step 1 - gradient.Step 2 - evaluate at the origin.Step 3 - unit vector towards .Step 4 - directional derivative.Rounded to the nearest integer this is .Note on accepted answers. If the direction vector is used without normalising it, the dot product gives . Because the question does not say explicitly that a unit direction is meant, both and are accepted for this question; the standard directional derivative (per unit distance) is the obtained above.Answer: (the exact value is ; is also accepted)
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