To find the directional derivative of a function at a point in the direction of another point, we need to compute the dot product of the gradient of the function at that point and the unit vector pointing from the first point to the second point.
1. Compute the gradient of the function at the given point, p.
The gradient of a function is a vector that consists of the partial derivatives of the function with respect to each variable. If the function is given by f(x, y, z), the gradient is represented as ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z).
2. Determine the unit vector pointing from the point p to the point q.
To find the unit vector, we subtract the coordinates of point p from the coordinates of point q, and then divide the resulting vector by its magnitude. This will give us a vector pointing in the direction from p to q with unit length.
3. Take the dot product of the gradient and the unit vector.
The dot product of two vectors is computed by multiplying the corresponding components of the vectors and summing the results.
The resulting value will be the directional derivative of the function at point p in the direction of point q.
It's important to note that you haven't provided the specific function or the points p and q, so I'm unable to provide a numerical example. However, if you provide the necessary details, I can guide you through the process of finding the directional derivative.
Please let me know if there is anything else I can help you with.