# How do you find F'(x) given F(x)=int tant dt from [0,x]?

Dec 19, 2016

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

#### 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

$F \left(x\right) = {\int}_{0}^{x} \tan t \setminus \mathrm{dt}$

Then

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

Dec 19, 2016

$\tan x$

#### Explanation:

When you are taking the derivative of an intergral, it is just the equation inside.
$F \left(x\right) = \int \tan t \mathrm{dt}$
${F}^{'} = \tan \left(t\right)$

All you have to do now is find out where your limits are from.

$\tan 0 = 0$
$\tan x = \tan x$
$\tan x - o = \tan x$