Find the Directional derivative of the function u

In summary, the conversation involves a request for verification of a directional derivative calculation. The attempt at solving the problem is deemed correct except for a minor error that was later corrected.
  • #1
asi123
258
0

Homework Statement



Hey.
I need to find the Directional derivative of the function u, in the direction l, in the point m (all in the pic).
I'm not sure I did it right, can you please give me the ok?


Homework Equations





The Attempt at a Solution


 

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  • #2
Up to DLu= (1/3)(2x- z)+ (2/3)cos y+ (2/3)x, everything looks good. Then you evaluate that at [itex](1,\pi/2, -3)[/itex] and get 7/10? That's not what I get.
 
  • #3
HallsofIvy said:
Up to DLu= (1/3)(2x- z)+ (2/3)cos y+ (2/3)x, everything looks good. Then you evaluate that at [itex](1,\pi/2, -3)[/itex] and get 7/10? That's not what I get.

Oops, got 7/3?
 
  • #4
Yes, that is correct. I wondered where that "10" came from!
 
  • #5
HallsofIvy said:
Yes, that is correct. I wondered where that "10" came from!

Broken calculator...:smile:

No, just kidding, it was early in the morning.
 

1. What is a directional derivative?

A directional derivative is a measure of the rate of change of a function along a specific direction. It tells you how much the function changes as you move in a particular direction from a given point.

2. How is the directional derivative calculated?

The directional derivative of a function u at a point (x,y) in the direction of a unit vector v is given by the dot product of the gradient of u at (x,y) and the unit vector v.

3. What is the significance of the directional derivative?

The directional derivative is important because it helps us understand the direction in which a function is changing the fastest at a given point. This can be useful in optimization problems and in understanding the behavior of a function in a certain direction.

4. Can the directional derivative be negative?

Yes, the directional derivative can be negative. This means that the function is decreasing in the direction of the unit vector v at the given point.

5. How is the directional derivative related to the partial derivatives?

The directional derivative is related to the partial derivatives through the chain rule. The partial derivatives in the x and y directions can be thought of as the directional derivatives in the x and y directions, respectively.

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