Hi I need help with calculus, thank you.

(1 point) Dierentiate the following function: u=W3 :3 {1 point} The displacement of a particle on a vibrating string is given by the equation 3(t) = 15 + 51154 121d), where s is measured in centimeters and t in seconds. Find the velocity of the particle attert seconds. 0(t) = (1 point) For what values of a: in [0, 211'] does the graph of x) = a: + 2 sins: have a horizontal tangent? List the values of as below. Separate multiple values with commas. z: (1 point) (a) Let f(:c) = sin\"(z). Find f'(:c). f '(I) = (b) Let f(s:) = since-4). Find 3'13). ft!) = (1 point) Find the derivative of we)\" Assume that a. and b are constants. 153(2) = (1 point) Let F(x) = f(f(x) ) and G(x) = (F(x))2 and suppose that f(6) = 4, f(4) = 3, f'(4) = 8, f' (6) =8 Find F' (6) and G' (6). F'(6) = G' (6) = (1 point) If f(x) = 4x3 arctan(8x4), find f' (x). f' (x) = Calculate g(b) and g'(b), where g is the inverse of f = x + sin(x) where b = 0. g (b) = g' (b ) =Tm children are playing on the swings in the friendly neighbourhood park. A claim is made by a student that the swing can be modeled by forced harmonic motion (i.e. simple harmonic motion that is being pushed}. Using this model. the horizontal position P of the swing relative to center of the swing structure is given by: P = Aka) . cos(wt) where t is time (in seconds). to is the frequency (in radians per second) at which the swing is pushed. and the direction the children are facing is the positive direction. Also, A is the amplitude (in meters) of the swing. as a function of or: 5 '4'\") = W In summary. at time t and with a pushing frequency of u. the horizontal distance of the swing from the centre line. is given by P = AM) cos(wt). 1. Find g. At pushing frequency w = 1 is this derivative positive. negative. or zero. and what does this indicate physically? 2. Now suppose w is constant. . (LP (121' . . (a) Fll'ld E and W. What do these dematwes represent? :1? (PP . . . . (b) Evaluate I and F for t = 355 and u = 1. Use your answers to determine whether the swung Is speeding up or slowing down. and in which direction