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GATE 2026 Chemical Engineering, Q21 · Mathematics

The correct answer is B, 14î + 10ĵ.

Question

A two-dimensional temperature profile is given as T =2x2+= 2x² + 3xy +y2.+ y². If î and ĵ are the unit vectors along x and y directions, respectively, which one of the following is the directional derivative of T at the location x = 2, y = 2?

  • A. 8î + 12ĵ
  • B. 14î + 10ĵ
  • C. 8î − 12ĵ
  • D. 14î − 10ĵ

Official answer: 14î + 10ĵ

Why

GATE 2026 official key: (B). ∇T=\nabla T = (4x+3y)î + (3x+2y)ĵ; at (2,2) this is (8+6)î + (6+4)ĵ = 14î + 10ĵ.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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