Let f(x) and g(x) be functions which are differentiable at all points in some interval, (a,b). If f ′
(x)=g ′
(x) for all x in the interval (a,b) then there is some constant, c, such that f(x)=g(x)+c for all x in the interval (a,b). Given the following pairs of functions, compute their derivatives to verify that f ′
(x)=g ′
(x) on the given interval. The aforementioned fact will imply that there is some constant c with f(x)=g(x)+c. Give the exact value of c for each pair of functions listed below. - f(x)=ln(3x) and g(x)=ln(x) on the interval (0,[infinity]). - f(x)=tan 2
(x) and g(x)=sec 2
(x) on the interval (− 2
π
, 2
π
).