Thread: directional derivative Help

Consider the function .
Find the the directional derivative of at the point in the direction given by the angle . Find the unit vector which describes the direction in which is increasing most rapidly at .

i could get the directional derivative which is -12. but how to get the unit vector out of it?

Originally Posted by zpwnchen

i could get the directional derivative which is -12. but how to get the unit vector out of it?

The direction of maximum rate of change is given by evaluated at the given point. Divide this vector by it's magnitude to get a unit vector.

gives the max rate of change.

so i find the


and then take a magnitude of it and gives me 1. so unit vector is going to be "-12" which is not right. :{

Originally Posted by zpwnchen

gives the max rate of change.

so i find the


and then take a magnitude of it and gives me 1. so unit vector is going to be "-12" which is not right. :{

I don't have the faintest idea what you're doing or why you're doing it.

The given function is . I have already told you that evaluated at the given point is the direction of maximum rate of change. And I have also told you to divide that vector by it's magnitude to get a unit vector in that direction.

I cannot see that you have done or attempted to do any of what I said.

By the way, "-12" is a scalar not a vector.

got it! thank you so much