Derivatives Review Quiz

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

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)

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

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

Find y' if y=e^3x

• e^3x
• e^2x
• 0
• 3e^3x

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

Find the slope of the tangent line to the curve

 $y=4-3x^2\ at\ \left(-1,1\right)$  .

• 4

• 5

• 6

• 7

Find the equation of the tangent line to the curve $y=x^2-3x+3\ at\ \left(3,3\right).$  

•  $y=3x-3$  

•  $y=x-3$  

•  $y=3x+3$  

•  $y=x+3$  

Find the equation of the tangent line to the curve $y=\left(3x^2+5\right)^2\ at\ \left(1,1\right).$  

•  $y=96x-95$  

•  $y=26x-25$  

•  $y=86x-85$  

•  $y=56x-55$  

Find dy/dx  if     12x + 4y = 10

•  $\frac{dy}{dx}=-\frac{1}{3}$  

•  $\frac{dy}{dx}=-\frac{1x}{3y}$  

•  $\frac{dy}{dx}=-3$  

•  $\frac{dy}{dx}=\frac{1}{3}$