Let g(x) be the integral of cos(t)/t from 6 to x, Find the derivative of g?

Question

should it not just be the function? cos(t) / t or.. cos(x) / x please explain thanks

Answer 1

integral of cos(t)/t
sorry . .its integral
let u = 1/t = t ^-1 . . . . . dv = cos t
du = -t^(-2) . . . . . . . v = sint t dt

integral of cos(t)/t = sin t / t - integ (sin t cost ) dt
. . . . = sin t / t - 1/2 sin ² t + c

Answer 2

g'(x) = cos (x)/x, by the Fundamental Theorem.