Question

Difference between directional derivative and partial derivative

Answer 1

Answer:

First of all gradient is a vector quantity where as Directional derivative is scalar quantity. For a function u= f(x,y) the partial derivative wrt x gives the rate of change of f in the direction of x and similarly for y also. ... Hence Directional derivative is dot product of the gradient and vector "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. ... For a general direction, the directional derivative is a combination of the all three partial derivatives.