- #1

mcastillo356

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The book is "Calculus" 7th ed, by Robert A. Adams and Christopher Essex. It is about an explained example of the first conclusion of the Fundamental Theorem of Calculus, at Chapter 5.5.

I will only quote the step I have doubt about:

**Example 7**Find the derivatives of the following functions:

(b) ##G(x)=x^2\,\displaystyle\int_{-4}^{5x}{\,e^{-t^2}\,dt}##

**By the Product Rule and the Chain Rule,**

*Solution*$$G'(x)=(...)$$

$$ =2x\displaystyle\int_{-4}^{5x}{\,e^{-t^2}\,dt}+x^2\;e^{-(5x)^2}\,(5)$$

When I've seen this last written (5), I've thought in first place that I had to move backwards in the textbook. At last, I've understood it referred to the integral upper limit.

Question: I've spent a few hours trying to understand the footnote: the number we must multiply the second summatory by.

Wouldn't it have been easier to just avoid this note and show the result, without that step? Furthermore: isn't this step unclear?.

Greetings!