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

2 Answers
Dec 19, 2016

Answer:

# 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

Answer:

#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#