Calculation of the derivatives of and
Problem formulation
Given functions
Complex analysis approach
Let us consider a function
Here,
Then, the
Linear algebra approach
Let us consider another approach that, from my point of view, is less efficient but is quite interesting.
Let us consider a set of all linear combinations of functions
Now, let us differentiate a function
The latter means that the differentiation operator
Thus, for
Then,
where operator
Calculating
If
Let us calculate eigenvalues
Calculating the derivative
Now, we can calculate the derivative of
which is the same result we obtained with complex analysis approach.