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

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