A. Find the derivative of each of the following functions:

1. f(x)= (2x² + 5x) ((3x+1) / (x³ - 2))
2. y(x)= (2x⁴ - 7) / (x² + x - 3)
3. g(x)= (3x² - 3x + 12) (x⁴ - x² + x - 1)
4. g(x)= 3 csc x
5. f(x)= 5x² sinx
6. y= 2 cosx tanx

B. A ball is thrown vertically upwards. Its height above the ground (in feet) after t seconds is given by s(t)= -16t² + 64t

1. What is the average velocity of the ball during its first 2 seconds in the air?
2. What is the instantaneous velocity of the ball 2 seconds after it is thrown?

C. A particle moves along a coordinate axis with its positive direction to the right. Its position at time t is given by s(t)= t³ - 3t² - 5t +5

1. Is the particle moving from left to right or right to left at time t= 2 ?
2. Is the particle speeding up or slowing down at time t= 2 ?

D. Find an equation for the tangent line of f(x)= sinx at x=pi/3 (x=3.14/3).