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

2 Answers
Dec 19, 2016

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

Dec 19, 2016

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