# Help required for Directional derivatives

1. May 6, 2012

### 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 Im 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?

2. May 6, 2012

### tiny-tim

hi hivesaeed4!

(try using the X2 button just above the Reply box )
no, u must be the unit vector

3. May 6, 2012

### hivesaeed4

I hope this does'nt 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.

4. May 6, 2012

5. May 6, 2012

### 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?

6. May 6, 2012

yup!

7. May 6, 2012

### hivesaeed4

Thanks alot, tiny-tim.