Based on the information provided, the step-by-step solution to this question is:
1. Start by defining the given angle, which is 45 degrees.
2. Next, you need to convert this angle from degrees to radians because the trigonometric functions in the following step naturally work in radians. In this case, the equivalent of 45° in radians is approximately 0.785398163.
3. Now, define the direction vector in polar coordinates. This is done using cosine and sine functions of the angle in radians. Since we are assuming that unit length, i.e., r=1, the direction vector will be: [cos(0.785398163), sin(0.785398163)]. The result of these calculations will yield the direction vector approximately [0.70710678, 0.70710678].
4. The following steps in the procedure assume the knowledge of the mathematical function f and of the function ‚àá(p), which are not given. If those were known, we would proceed this way:
5. Compute the gradient of the function f. The gradient is a vector that points in the direction of the greatest rate of increase of the function. It is denoted by grad_f.
6. After that, compute the dot product of the gradient and the direction vector. The dot product will result in the rate of change of function f in the direction of the vector. This result is indicative of how much the function changes if one moves along the direction vector.
Please note that since the functions f and ‚àá(p) aren't provided, the actual calculations can't be performed. However, the steps given are the general procedure to solve such problems.