# directional derivative

• October 31st 2012, 05:17 AM
prasum
directional derivative

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
• October 31st 2012, 05:57 AM
HallsofIvy
Re: directional derivative
The directional derivative is $\nabla f$ 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 $2\sqrt{3}$. Find the gradient of f at (2, -1, 0), take its dot product with $<-1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}>$ and, finally, multiply by the distance moved, .2.