Posted by **Dani** on Sunday, February 27, 2011 at 11:31pm.

The directional derivative of z = f(x,y) at (2,1) in the direction toward the point (1,3) is -2/sqrt(5), and the directional derivative in the direction toward the point (5,5) is 1. Compute dz/dx and dz/dy at (2,1).

I have no idea how to solve this problem. Help, please? Thank you.

- Calc -
**agrin04**, Monday, February 28, 2011 at 2:31am
From point (2,1) to (1,3):

u = <1-2,3-1> = <-1,2>

Note that vector u above is not a unit vector, so we need to make this a unit vector by dividing it with its magnitude.

u = <-1,2>/sqrt(5)

<dz/dx,dz/dy>•<-1/sqrt(5),2/sqrt(5)> = -2/sqrt(5)

-dz/dx + 2dz/dy = -2. ..(1)

From point (2,1) to (5,5):

v = <5-2,5-1> = <3,4>

Again, this is not a unit vector.

v = <3,4>/5 = <3/5,4/5>

<dz/dx,dz/dy>•<3/5,4/5> = 1

3dz/dx + 4dz/dy = 5. ..(2)

Using elimination and substition to both equations (1) and (2), you'll get the value for dz/dx and dz/dy

## Answer This Question

## Related Questions

- Calc - "Let f(x,y)=2(x^2)y-(y^3)+x-4. a) Find the local linearization of f at (3...
- mathematical physics - Determine the directional derivative of phi =xy^z in the ...
- cal3 - Consider the function f(x,y)=xy+xz+yz+4 at point p=(2,-1,1) a)find the ...
- Directional derivative - "Find the directional derivative fu(1,2) for the ...
- CALCULUS - Find the gradient and directional derivative of f at P in the ...
- calc - 3. If f(x, y)=5 − 4x3 + 8y2, find a unit vector ~u for which the ...
- Environmental Science - I have to determine which kind of natural selection is ...
- math - consider a 2D mirror has a parabolic profile of y = (x-3)^2 + 5 facing ...
- math - please help me to solve this assignment : consider a 2D mirror has a ...
- Electricity - suppose that you're facing a straight current carrying conductor, ...

More Related Questions