# Finding a Unit Vector and Direction

• November 6th 2011, 08:32 PM
Number42
Finding a Unit Vector and Direction
Hi,

I need to find the directional derivative of a function. I know how to do this, the problem with this particular question is that the point given is

$(x,y) not equal to (0,0)$

and the direction given is "toward the origin."

I know to find the directional derivative is simply using the dot product between the gradient of f and the unit vector, but I don't know how to determine what the unit vector here is exactly.

Oh, the function is

f(x,y) = ln sqrt(x^2 + y^2).

• November 6th 2011, 11:34 PM
FernandoRevilla
Re: Finding a Unit Vector and Direction
Quote:

Originally Posted by Number42
$(x,y)\neq (0,0)$ and the direction given is "toward the origin."

$(0,0)-(x,y)=(-x,-y)$ so, use $u=-\dfrac{1}{\sqrt{x^2+y^2}}(x,y)$
• November 7th 2011, 12:54 AM
Number42
Re: Finding a Unit Vector and Direction
Quote:

Originally Posted by FernandoRevilla
$(0,0)-(x,y)=(-x,-y)$ so, use $u=-\dfrac{1}{\sqrt{x^2+y^2}}(x,y)$

¡Gracias, mi amigo! That is exactly the breakthrough I had been looking for. I've been at this for two days now.

Thank you once again! (Rofl)(Rock)
• November 7th 2011, 01:14 AM
FernandoRevilla
Re: Finding a Unit Vector and Direction
Quote:

Originally Posted by Number42
¡Gracias, mi amigo!