Directional Directives and the Gradient Vector

Purpose is to find the rate of change from a point (x,y) in direction (a,b) for a given function f(x,y)

the partial derivative of function f(x,y) is put in a vector form

the point (c,d) is put into it into the partial derivative of f(x,y) in vector form

the unit vector of direction (a,b) is multiplied to above

This gives the directional derivative:

☀http://mathworld.wolfram.com/DirectionalDerivative.html

Rate is modulus(distance function) of gradient

Direction is just the gradient