Integration & Differentiation Practice

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx

• f"(x) = 2x + e^x + cosx

• f"(x) = 2x + xe^x - cosx

• f"(x) = 2x + e^x + sinx

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)

Find the derivative.
 f(z) = 1/(3z²) + 4z³

• f'(z) = 6z³ + 12z²

• f'(z) = 6z + 12x²

• f'(z) =  -2/(3z³) + 12z²

• f'(z) = -6/z² + 12z²

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)

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

• A

• B

• C

• D

• A

• B

• C

• D

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