Derivatives Test Review

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)

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

d/dx (sin²x) = ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

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)

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)