Thread: directional derivative

by about how much will

g(x,y,z)=x+x*cosz-y*sinz+y

change if the point p(x,y,z) moves from p(initial)=(2,-1,0) a distance of ds=0.2units towards the point p(final)=(0,1,2)

i know we have to find df here

directional derivative=df/ds

but how to use above information to establish the result

The directional derivative is dot product a unit vector in the given direction. Since the given direction is from (2, -1, 0) to (0, 1, 2), the vector from the first to the second is <-2, 2, 2> which has length . Find the gradient of f at (2, -1, 0), take its dot product with and, finally, multiply by the distance moved, .2.