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Really there is no problem to go with this question just something that I was discussing awhile back but was never really cleared up, what is the difference between:

[tex] d(\int^{x}_{a} f(t)dt) = f(x) dx [/tex]

and

[tex] \frac{d}{dx}\int^{x}_{a} f(t) dt = f(x) [/tex]

I understand that the top equation is called the differential form and the bottom is the derivative form and really thats about it. I was told that they were different by a factor of dx such that:

[tex] df = \frac{d}{dx}*dx [/tex]

but I really don't understand how that makes any difference because if dx is infinitely small how does that affect the answer of the problem?

This arose from the book that I am using introducing The Fundamental Theorem of Calculus with the differential form and not the derivative form which evidently is the norm. I really just want a little clarification on this issue and apologize in advance if this is something quite obvious.

Thanks!

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# Homework Help: Differential vs derivative explained

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