Walter rudin 9.32

Question

There are the theorem and its proof :

$\mathscr b'$ mapping means continuously differentiable function.

I don't understand how do we get (76) from (71). If this is so then it means that ($PF(H(X))$)' = $P(F(H(X))'$ But from where we can say that this is true?

Any help would be appreciated.

Answer 1

It will be the same as the derivative of $\frac d{dx}(Ax)$ and it's equal of $A.$