Directional Derivative Applet

This applet estimates the directional derivative Du at a point (p,q) in the direction of a nonzero vector v.  The directional derivative Du is the slope of the tangent line at (p,q) to the curve formed by the vertical slice of the surface z = f(x,y) in the direction of v.  

Enter f(x,y) as a function of x and y:      f(x,y) =

Enter plot settings. The y settings can be either numbers or functions of x:

x min:       y min(# or g(x) ):      Grid (x) :    Axes:
x max:    y max(# or g(x) ): Grid (y) :
 

Enter a point and a  vector.  The vector v will be normalized into a unit vector u.

point (p,q) =      ,                              vector v =     ,  
 

The Plot button below will create a new window with the surface z = f(x,y), the vertical slice along u = v/||v||, the curve formed by the vertical slice, and an estimate of Du for the given point.