The Fundamental Theorem of Calculus Suppose f is continuous on [a, b]. 1. If g(x) = [:f (1) dt, then g'(x) = f(x). . Saf(x)dx = F(b) - F(a), where F is any antiderivative of f, that is, F'= f. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. F ( x ) = V1 + sec (5t) dt Hint : / V 1 + sec ( 5t ) at = - V1 + sec(5t) dt F' ( X ) = Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = 43 3 x 1+ 42 - du y' Find the derivative of the function. 9 ( x ) = / 4 2- I au [mint : for rus an = forus an + fox run au] g'( x ) = Find the derivative of the function. sin(x) y = In(3 + 4v) dv cos(x) y' ( x ) =