11 questions to be answered

If f(z) = 4sin x + 8 cos x, then f'(2) = To two decimal places, f' (5) = If f(x) = 5x(sin x + cos z), find f' (x) = To two decimal places, f' (4) = If f(z) = cos x - 3 tan x, then f' (x) = To two decimal places, f' (3) - Find the derivative of y(x) = 2tana + 2 cot x. Use trigonometric identities cos' a = - 1 + cos(2x) 1 - cos(2x) much as possible. 2 - and sin a = 2 - to simplify as y'(x) = Use the quotient rule to find the derivative of f(x) = _10 sin(z) + 10 3x7- 1 You do not need to expand out your answer. Be careful with parentheses! f'(x) = Question Help: Video .Written Example Message instructor Submit Question If f(z) = 4x sin x cos x, find f'(z)= To two decimal places, Let f() = cos(x), find each of the following: Find f' (1) = Find the second derivative, f' '(z) - If f(x) 4x tanx -, find sec x Find the third derivative, f" " '(x) = f'(x) = To two decimal places, Find the fourth derivative, f' ' ''(x) = Find f' (2)= Find the equation of the tangent line to the curve y = 2 sin a at the point ( , 1). The equation of this tangent line can be written in the form y = ma + b where (to two decimal places) m= and b = A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 2 cost where s is measured in centimeters and t is measured in seconds. Find the rate at which the spring is oscillating at t = 6 s. Round your answer to four decimal places. cm/ s A mass of mass 90 g is attached to a massless spring and undergoing simple harmonic motion on a frictionless table. The position of the mass is given by z(t) = - sin(t). The amplitude of the motion is - 1 cm and time is in sec. a.) Determine the velocity u(t) of the mass in u(t) = b.) Determine the acceleration a(t) of the mass in (sec)? a(t) = sec c.) Calculate the velocity at t = 5: in . Round to 3 decimal places as needed. U(5TT) = d.) Calculate the speed at t = 5 in one, Round to 3 decimal places as needed. speed =