Help required for Directional derivatives

[hivesaeed4]

f=9-x^2-y^2 and u=i-j
The directional derivative comes out to be Du f(x,y)=-sqrt(2)+sqrt(2)

I'm going to find the directional derivative and could someone kindly point out the mistake because I am getting a different answer and it's important I understand how to do this question:

Du f(x,y) is simply the ∇f.u (note u is a vector)

Now ∇f=-2xi-2yj and ∇f.u=(-2xi-2yj).(i-j) = -2x+2y. Help?

 

[tiny-tim]

hi hivesaeed4!

(try using the X² button just above the Reply box )

Du f(x,y) is simply the ∇f.u (note u is a vector)

no, u must be the unit vector

 

[hivesaeed4]

I hope this doesn't sound stupid but does u always have to be a unit vector. The reason I'm asking is that this is the first time I've heard of it having to be a unit vector.

 

[tiny-tim]

… does u always have to be a unit vector.

yes!

see eg http://en.wikipedia.org/wiki/Directional_derivative#Definition

 

[hivesaeed4]

So instead of having taken the dot product of u and del of f in the above example I should have taken the dot product of del of f and the unit vector of u.

Right?

 

[tiny-tim]

yup!

 

[hivesaeed4]

Thanks alot, tiny-tim.