Find F'(x) (Find derivative of integral)

Calculus
Tutor: None Selected Time limit: 1 Day

F(x)= intergal (bottom) to (top) as x goes to x^2 

sec^2 t dt

Apr 28th, 2015

d(tant)/dt=sec^2t dt

so the integral of sec^2 tdt = tant








Apr 28th, 2015

That isn't one of the answer choices

Its more detailed I believe

Apr 28th, 2015

I believe you know have to plug in what the integral goes to

Apr 28th, 2015

please clarify what integral goes from i am not able to get it....is it from x to x^2


Apr 28th, 2015


Apr 28th, 2015
fullsizerender_3.jpg

answer should be A)






Apr 28th, 2015

Can you show how you got this answer? I need to know how to work the problem

Apr 28th, 2015

the answer of integral is

(tant)  from x to x^2

i e tanx^2-tanx


now we have to differentiate the function tanx^2- tanx


Apr 28th, 2015

now we will get,

d/dt(tanx^2-tanx)=2xsec^2 x^2-sec^2x

                           =2x.secx^2.sec^2 -secx.secx



so answer is B sorry for mistake.

Apr 28th, 2015

did u get????

Apr 28th, 2015

Can you break down your derivative steps

Apr 28th, 2015

ok.

  d/dt(tanx^2-tanx)=   d/dt(tan(x^2))-d/dt(tanx)         but we know that d/dt(tanx)=sec^2 (x)

             so                =  sec^2(x^2) .d/dt(x^2)  -sec^2(x)                      ( use chain rule of derivative)

                                 =2xsec^2 (x^2)-sec^2x

                                 =2x.sec(x^2).sec(x^2)   -  secx.secx


Apr 28th, 2015

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