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The quotient rule worksheets Grade 12

Differentiate quotients with the quotient rule.

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Free · Worked example · 29 problems · Answer key · US Letter

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How to do it

(u ÷ v)′ = (u′v − uv′) ÷ v². Leave the denominator squared.

f(x)=4x−7x+5f′(x)=27(x+5)2f(x) = \dfrac{4x - 7}{x + 5}\quad f'(x) = \dfrac{27}{(x + 5)^{2}}
f′(x)=4(x+5)−(4x−7)(1)(x+5)2f'(x) = \dfrac{4(x + 5) - (4x - 7)(1)}{(x + 5)^{2}}(u/v)′ = (u′v − uv′) ÷ v²
4(x+5)−(4x−7)(1)=274(x + 5) - (4x - 7)(1) = 27the x terms cancel in the numerator

Example problems

  1. f(x)=−5x−8x−8f′(x)=f(x) = \dfrac{-5x - 8}{x - 8}\quad f'(x) =
  2. f(x)=−2xx+5f′(x)=f(x) = \dfrac{-2x}{x + 5}\quad f'(x) =
  3. f(x)=−x+5x+8f′(x)=f(x) = \dfrac{-x + 5}{x + 8}\quad f'(x) =
  4. f(x)=−x+9x−5f′(x)=f(x) = \dfrac{-x + 9}{x - 5}\quad f'(x) =

Limits and derivatives

  1. Evaluating limits
  2. The power rule for derivatives
  3. The product rule
  4. The quotient rule
  5. The chain rule
  6. Derivatives of trig, exponential and log functions
  7. Equation of a tangent line
  8. Derivatives as rates of change
  9. Finding maximum and minimum points