Find f '(0.3) for f(x)=the integral from 0 to x of the arccosine(t)dt

    if we let  , then    by the fundamental theorem of calculus, with  as the antiderivative of      differentiating both sides with respect to x (g(0) is a number; derivative of that is 0), we get    really, the antiderivative of a function is a function that when differentiated gets the original function, hence the jump from g'(x) to g(x).so f'(0.3) (in radians)  is    approximately 1.26610