Question

How do you use part one of the fundamental theorem of calculus to find the derivative of the function `g(x)= intcos(t^10) dt` from [cos(x) to 10x] ?

Answer 1

Refer to explanation

Explanation:

It is

#g(x)=int_cosx^(10x) cos(t^10)dt=> (dg(x))/dx=cos((10x)^10)*(d(10x))/dx-cos((cosx)^10)*d(cosx)/dt= 10*cos((10x)^10)+sinx*cos((cosx)^10)#

Generally if have a function with formula

`g(x)=int_g(x)^(k(x)) f(t)dt` then its derivative is

`(d(g(x)))/dt=f(k(x))*((dk(x))/dt)-f(g(x))*((dg(x))/dt)`