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GATE Engineering Mathematics: Calculus: Directional derivatives – Previous Year Questions

5 GATE previous year questions on Calculus: Directional derivatives (Engineering Mathematics, Electrical Engineering) with answers and explanations, from every paper.

  1. GATE 2018 EE Q22 (1 mark, Multiple choice) – The value of the directional derivative of the function (x,y,z)=xy2+yz2+zx2 at the point (2,-1,1) in the direction of the vector p= i+2 j+2 k is
  2. GATE 2022 EE Q50 (2 marks, Multiple choice) – Let, f(x,y,z)=4x2+7xy+3xz2. The direction in which the function f(x,y,z) increases most rapidly at point P=(1,0,2) is
  3. GATE 2023 EE Q65 (2 marks, Numerical answer) – A quadratic function of two variables is given as f(x 1,x 2)=x 12+2x 22+3x 1+3x 2+x 1x 2+1 The magnitude of the maximum rate of change of the function…
  4. GATE 2024 EE Q36 (2 marks, Multiple choice) – Consider a vector u=2 x+ y+2 z, where x, y, z represent unit vectors along the coordinate axes x,y,z respectively. The directional derivative of the…
  5. GATE 2025 EE Q53 (2 marks, Numerical answer) – Let (x,y)2. The rate of change of the real valued function, V(x,y)=x2+x+y2+1 at the origin in the direction of the point (1,2) is (round off to the…