Calculus Final Exam

The _______ is used to differentiate composite functions.

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 the derivative of f(x)=(x³ - 2x)²

and simplify

• 6x⁵ - 12x³+8x

• 6x⁵ - 16x³+8x

• x⁶-4x⁴+4x²

• 6x⁵ - 16x^3-8x

What is the derivative of cot(x)?

• sec²(x)
• -sec²(x)
• csc²(x)
• -csc²(x)

What is the derivative of sin(x)?

• -sin(x)
• -cos(x)
• cos(x)
• sin(x)

sin^-1(-1/2)

• π/3
• π/6
• 5π/6
• -π/6

tan^-1(√(3))

• π/3
• 2π/3
• π/6
• 5π/6

sin^-1(-1) =

• π/2

• 0

• -1

• -π/2

cos^-1(0) = 

• π/2
• π
• 1
• none of these