Derivatives

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)

• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t

What is the acceleration of the object at time t = 2 s?

• 64 m/s/s

• 60 m/s/s

• 66 m/s/s

• 70 m/s/s

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2

• 3(x²+2)/(x²+2)²

• (-3x²+4x +6)/(x²+2)²

• (-3x²+10)/(x²+2)²

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²

• 18x² - 16x

• 15x² - 6x

• 6x - 4

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?

• v = 0

• v = 1

• v = -1

• v = -2

Find the derivative

f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴

• f'(t) = 5(t² + 2t)⁴

• f'(t) = 5(t² + 2t)⁴(2t)

• f'(t) = 5(t² + 2t)⁴(2t + 2)

The equation of the tangent to y=1/x at x=3 is

• y=-1/9x+2/3

• y=1/3x+1/3

• y=1/9x+9

• y=1/9x

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx by Implicit Differentiation
xy = 6

• -x/ y
• -y/ x
• -6y/ x
• y/x

Differentiate:

f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)

• f '(x) = x⁶ (5 + 8x)² (35 + 80x)

• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)