Derivative Drills 1

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

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

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

• 38 m/s/s
• 27 m/s/s
• 16 m/s/s
• 49 m/s/s

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 y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Find y' if y = cos⁵(4x³)

• -5cos⁴(4x³)sin(12x²)
• -60x²sin⁴(4x³)
• -5cos⁴(4x³)sin(4x³)
• -60x²cos⁴(4x³)sin(4x³)