Directional Derivatives gradient divergence and curl Vector Calculus Gate 2021 Mathematics

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Vector Calculus: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes, and Gauss theorems.

Directional Derivatives gradient divergence and curl Vector Calculus Gate 2021 Mathematics
Question

Let f∶R^2→R be differentiable.Let D_u f(0,0) and D_v f(0,0) be the directional derivatives
of f at (0,0) in the directions of the unit vectors u=(1/√5,2/√5) and v=(1/√2,-1/√2),respectively.
If D_u f(0,0)=√5 and D_v f(0,0)=√2 then ∂f/∂x (0,0)+ ∂f/∂y (0,0)=⋯

En Gate MA 2021, 15
Key (4)
  1. Harvard University Entrance Exam PYQs
  2. directional derivative
  3. directional derivative and the gradient vector
  4. directional derivative in vector calculus
  5. directional derivative of a function of two variables
  6. directional derivative problems
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