Calculus Animations,Graphics and Lecture Notes Directional Derivatives/Gradient
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The following animations and lecture notes discuss the directional derivative

In Animation1 We see the rate at which f is changing at a point depends on the direction we travel from the pt

Notes - Directional Derivatives and the Gradient

Animation1

 The following 2 animations show f changing in the diection of the gradient and opposite to the gradient gradient negative gradient The following Animation shows that as you move along a level curve in the domain, there is no change in the value of f(x,y) on the surface. Motion Along a Level Curve

The Smart Bunny-A very short story by Kurt Vonnegut Jr.