AP Calc 10/13: Product/Quotient Rule Practice

Find the derivative of g(x)=(3x-2)/(x²+2)

• 3/(2x)
• (-3x²-4x +6)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• slope of the secant line

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Find the derivative: y=^-1/_x

• -1
• 0
• ^1/x²
• x

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

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

• 12x⁴ +3x²

• 20x⁴ +3x² +16x

• 3x⁵ +32x³ +6x² +8x

• 24x³

• 8x⁴ -60x²
• 16x⁴
• (8x⁴ -60x²)/(2x²-5)²
• 3x

Given f(x) = ax² + 2bx. What are a and b if f'(x) = 8x + 6?

• a = 2 and b = 3

• a = 3 and b = 2

• a = 3 and b = 4

• a = 4 and b = 3

Given that y = (x+2)/(x-3), find y'.

• y' = -1/(x-3)²
• y' = -5/(x-3)²
• y' = (2x-5)/(x-3)²
• y' = (2x-1)/(x-3)²