Product and Quotient Rule

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

Given f (x) = 5sinx + 3x³cosx, f '(x) =

• -5cosx − 3x³sinx + 9x²cosx
• 5sinx − 3x³sinx + 9x²cosx
• 5cosx − 3x³sinx + 9x²cosx
• 5cosx + 3x³sinx + 9x²cosx

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

• cscx cotx
• secx tanx
• sec²x
• -cscx cotx

Find the derivative: y=^-1/_x

• -1
• 0
• ^1/x²
• x

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

Which one is the product rule?

• f(x)g(x)
• f'(x)g(x)-f(x)g'(x)
• f'(x)g(x)+f(x)g'(x)
• f'(x)g'(x)+f'(x)g'(x)

Which one is the quotient rule?

• [f'(x)g(x)-f(x)g'(x)]÷g(x)^2
• [f'(x)g(x)-f(x)g'(x)]
• [f'(x)g(x)-f(x)g'(x)]÷g(x)^4
  
• f(x)g(x)-f(x)g(x)]÷g(x)^2
  

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

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