algebra and calculus revision

Differentiate x^3/7 with respect to x.

• (3/7) x^-5/7

• (3/7) x^-3/7

• (-3/7) x^-4/7

• (3/7) x^-4/7

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

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

the slope of the tangent line at a function's local max will be

• undefined

• positve

• negative

• 0

Find dy/dx for

y = (x² + 1)³

• dy/dx = 3(x² + 1)²

• dy/dx = 12 x²

• dy/dx = 6x (x² + 1)²

• dy/dx = 2x(x² + 1)²

Simplify the following expression

• 3^2n-1

• 3²ⁿ⁺¹

• 3⁵ⁿ⁺³

• 3^5n-3

Write as a single fraction

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Simplify

• 6x - 9x³

• 2x² -3x⁴

• 2x - 3x³

• 3x³ - 2x

Find f'(x) given that f(x) is

• 2-9x²

• 3x²- 9

• 3x² - 2

• 12 x -36 x³

Write as a single fraction

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