# Calculating the directional derivative of a function of two variables

1. Nov 10, 2009

### wshfulthinker

The problem statement, all variables and given/known data

Consider the function:
z=f(x,y)= log(x^2 + y^2) (x,y)=/=(0,0)

Calculate the directional derivative of f(x,y) at (x,y)=(1,1) in the direction of the vector (1,2)

The attempt at a solution

When i tried to work out the unit vector from the point (1,1) to (1,2) i got (0,1).

I got partial derivative df/dx = 2x/(x^2 + y^2)
and partial derivative df/dy = 2y/(x^2 + y^2)

Then, for gradf at (1,1) i got (1,1)..

so, for directional derivative i got:

(gradf at (1,1)) x unit vector = (1,1).(0,1) = 1

Does anyone know what i have done wrong? Thankyou

2. Nov 10, 2009

### tiny-tim

Welcome to PF!

Hi wshfulthinker! Welcome to PF!

(have a curly d: ∂ and a square-root; √ and a grad: ∇ and try using the X2 tag just above the Reply box )
Nooo … you're msunderstanding "the direction of the vector (1,2)" …

it's not the point (1,2) (which is in direction (0,1) from (1,1), as you say) …

(1,2) is the actual direction that you're taking the derivative along.

(otherwise, your method is ok )

3. Nov 10, 2009

### wshfulthinker

Hi, thanks for the welcome and showing me the symbols!

I don't really get it though! where do i use the point (1,2). I'm not even sure what i worked out, i followed the method that were in my lecture notes which were worded almost the exact same way as my actual question (except it said find instead of calculate - i don't know if that means it's different)

4. Nov 10, 2009

### tiny-tim

grrr! it's not a point!!