Question

relation between directional and partial derivatives​

Answer 1

In fact, the directional derivative is the same as a partial derivative if u points in the positive x or positive y direction. For example, if u=(1,0), then Duf(a)=∂f∂x(a). Similarly if u=(0,1), then Duf(a)=∂f∂y(a).

Answer 2

Answer:

For a function z=f(x,y), the partial derivative with respect to x gives the rate of change of f in the x direction and the partial derivative with respect to y gives the rate of change of f in the y direction.

Explanation: