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

Dec 22, 2016

$F ' \left(x\right) = \frac{1}{x}$

#### Explanation:

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

$F \left(x\right) = {\int}_{a}^{x} f \left(t\right) \setminus \mathrm{dt} .$

Then:

$F ' \left(x\right) = f \left(x\right)$

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

So if we have

$F \left(x\right) = {\int}_{1}^{x} \frac{1}{t} \setminus \mathrm{dt}$

Then

$F ' \left(x\right) = \frac{1}{x}$