Consider the following. p = 2 9² +5 Зд - 2 Let u(q) = q² + 5 and v(q) = 3q − 2. Find each indicated derivative. u'(q) = v'(9) = Find each indicated product. v(q) · u'(q) = u(q) · v'(q) = Find dp dq dp dq II

Let s(t)= 8t^3−24t^2−192t be the equation of motion for a particle. Find a function for the velocity.v(t)= (ans) Where does the velocity equal zero? [Hint: factor out the GCF.]t= (ans) and t= (ans) Find a function for the acceleration of the particle.a(t)= (ans)

Use the quotient rule to find the derivative of the function. y= 3x+1 8x+7 What is the correct way of writing the derivative of y? d (8x+7). (3x+1)- (3x+ dx dx + 1). (8x+ d (8x+7) ○ A. y' = [(8x+ +7)]² d d (8x+7) • О в. dx (3x+1)− (3x+1)• ¯dx (8x+7) y' = -(3x+1) O C. y=- (8x+7) ○ D. y' = d -(8x+7)• dx [(8x+ +7)]² [(8x+7)]² (3x+1)

find the derivative of (2 + j)

Find the derivative of the function. y= 6x + 7 4x - 3 Which of the following shows how to find the derivative of the function? O A. y' = O B. y' = (6x +7) [ (4x-3) O C. y'=(6x +7) d dx OD. y'= (6x + 7) +7) (4x-3) - 7) ( = x (x + 71) dx (4x-3) d 1)(x (6x +7) - (6x +7) (4x - 3)) (4x-3) dx dx (4x - 3)² (6x +7)² The derivative is y'=0. d - 3)(x² dx (6x +7) +(4x-3) +(4x-3) (6x + 7) d dx (4x - 3) (x (4x-3) + (4x-3) ((x+7)) dx

Find y' and y'' for 2x3-5y2=8