A vector of 5√2 units in y- z plane is
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the point (x,y)=(3,2) are:
∂f∂x(x,y)∂f∂x(3,2)=2xy=12∂f∂y(x,y)∂f∂y(3,2)=x2=9
Therefore, the gradient is
∇f(3,2)=12i+9j=(12,9).
(b) Let u=u1i+u2j be a unit vector. The directional derivative at (3,2) in the direction of u is
Duf(3,2)=∇f(3,2)⋅u=(12i+9j)⋅(u1i+u2j)=12u1+9u2.(1)
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