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)