- #1
wshfulthinker
- 8
- 0
Homework Statement
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
But the answer is 3/root5
Does anyone know what i have done wrong? Thankyou
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
But the answer is 3/root5
Does anyone know what i have done wrong? Thankyou