exponential and logarithmic derivatives homework

If f(x) = sec(4x), then f'(x) =

• 4sec(4x)tan(4x)
• 2sec(4x)tan(4x)
• -4csc(4x)cot(4x)
• -2csc(4x)cot(4x)

Tags

CCSS.HSF.TF.C.8

If f(x) = 4tan(x/2), then f'(x) =

• 4sec²(x/2)

• -4csc²(x/2)

• 2sec²(x/2)

• -2csc²(x/2)

Tags

CCSS.HSF.TF.C.8

If f(x) = -csc(x/2), then f'(x) = 

• sec²(x/2)
• 2csc(x/2)tan(x/2)
• ½csc(x/2)tan(x/2)
• -csc²(x/2)

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

Tags

CCSS.HSF.IF.A.2

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

Tags

CCSS.HSF.IF.A.2

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

Tags

CCSS.HSF.IF.A.2

Find y' if y=e^3x

• e^3x
• e^2x
• 0
• 3e^3x

Tags

CCSS.HSF.BF.B.5

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

find y' for y=(e^5x)+1

• 5e^5x+1

• e^5x

• 5e^5x

• 1

Tags

CCSS.HSF-IF.C.8B

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)