How do you find #F'(x)# given #F(x)=int 1/t dt# from #[1,x]#?

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Answer 1 · 2016-12-22T20:08:30

# F'(x) = 1/x #

We apply the First Fundamental theorem of calculus which states that if (where #a# is constant).

# F(x) = int_a^x f(t)\ dt. #

Then:

# F'(x) = f(x)#

(ie the derivative of an anti-derivative of a function is the function you started with)

So if we have

# F(x) = int_1^x 1/t \ dt #

Then

# F'(x) = 1/x #