Thread: Leibniz Rule - quick question

I'm working through an example following Leibniz rule...but havning trouble following it:

We differentiate:



using Leibniz's Rule:



So just looking at the first integral,

I don't understand the b'(x)f(x,b(x)) part of the rule. Here b(x) = x so b'(x) = 1. But for f(x,b(x)) this would become f(x,x) right? I'm not sure why this is the same as y(x) though??

Thanks in advance!

There are 2 Leibniz's you have to apply:
both will generate:


Quickly applied the rule, and found:



I might have made a mistake. So be please becareful.

-O works then hopes.