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Engineering Mathematics
Linear Algebra
GATE 2011
Hard

Unit vectors in x and z directions are i and k respectively. Which ONE of the following is the directional derivative of the function F(x,z)=ln(x²+z²) at the point P:(4,0), in the direction of (i−k)?

  • Ai/(2√2)
  • Bi
  • C1
  • 1/(2√2)

Explanation

∇F=(2x/(x²+z²), 2z/(x²+z²)). At (4,0): (8/16,0)=(0.5,0). Unit vector along (i−k): (1/√2,−1/√2). Directional derivative=∇F·û=0.5×(1/√2)+0×(−1/√2)=0.5/√2=1/(2√2).

Source: GATE CH 2011 (2011)

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