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The product rule worksheets Grade 12

Differentiate products with (uv)′ = u′v + uv′.

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How to do it

(uv)′ = u′v + uv′. Then multiply out and combine like terms.

f(x)=(2x+3)(x+6)f′(x)=4x+15f(x) = (2x + 3)(x + 6)\quad f'(x) = 4x + 15
f′(x)=(2)(x+6)+(2x+3)(1)f'(x) = (2)(x + 6) + (2x + 3)(1)(uv)′ = u′v + uv′
(2)(x+6)+(2x+3)(1)=4x+15(2)(x + 6) + (2x + 3)(1) = 4x + 15multiply out and combine

Example problems

  1. f(x)=(3x)(2x+5)f′(x)=f(x) = (3x)(2x + 5)\quad f'(x) =
  2. f(x)=(x2−4)(4x+5)f′(x)=f(x) = (x^{2} - 4)(4x + 5)\quad f'(x) =
  3. f(x)=(x2+1)(3x−5)f′(x)=f(x) = (x^{2} + 1)(3x - 5)\quad f'(x) =
  4. f(x)=(2x+4)(2x−4)f′(x)=f(x) = (2x + 4)(2x - 4)\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