I am not studying maths, hence I need a little help with the algebra performed in the following image:
I can follow every step until equation 20. Basically my question is how to come up with 20, starting at 19.
I am not sure about that derivative. It confuses me that apparently this is the derivative wrt. a row vector. Furthermore I do not know how the individual parts come into the equation. Would someone be so kind and explain to me what is happening here? What is the role of the transpose p and why are the parts the way they are stated?
I need to obtain a similar sensitivity matrix for a project, so understanding how this equation arises is important for me.
Edit: Since I managed to come up with the left part, given a certain way to write a product rule, I asked this more general question here: Product-rule for Jacobian calculation, i.e. $\frac{d}{dx}(Ay)$ where A is a matrix and y a vector and both depend on x . See my third comment. I would really appreciate it if someone can tell me if it is okay to write the product rule like this.