If is continuously differentiable in , is continuously differentiable in , a constant real, how to calculate the derivative of with regard to (not by numerical methods)? Thanks.
After reading the proof of this general Leibniz integral rule, I have to stress that the conditions supporting the special case of Leibniz integral rule(*) must be preserved to make possible the interchange of the lim and int process in producing the integral part of the result when , the most important of which is the continuity of the partial derivative.
(*) where a,b are both constant.
ps: My question comes from the proof of Poincare's lemma in baby Rudin, the proof that is omitted as usual in Th10.38, I think the general Leibniz integral rule is necessary to prove it which is not mentioned at all in this book. I hope it is not the author's original intention to leave such a huge gap for me to fill. Thanks to Tonio I finally made it.