Question

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

Answer 1

`F'(x) = tanx`

Explanation:

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_0^x tant \ dt`

Then

`F'(x) = tanx`

Answer 2

`tan x`

Explanation:

When you are taking the derivative of an intergral, it is just the equation inside.
`F(x)=inttantdt`
`F^'=tan(t)`

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`