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Mathematics · Grade 11

Derivative Meaning and Rules

Learners define the derivative as a limit of difference quotients, interpret it with units, connect the graphs of f and f′, and learn where derivatives fail to exist. They then derive and apply the power, sum, product and quotient rules, use the derivatives of sine, cosine, the exponential and the natural logarithm, apply the chain rule, and write tangent lines.

  • 5 lessons
  • About 155 minutes
  • Derivatives check: 12 questions
  • Ways to answer: choose an answer, match pairs, type a number, put in order, sort into groups and true or false
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What learners will discover

  • Define the derivative as a limit, compute it from the definition, and interpret f′(a) with units.
  • Relate the graphs of f and f′ and identify where f is not differentiable, distinguishing differentiability from continuity.
  • Apply the power, constant-multiple, sum, product and quotient rules and the derivatives of sin x, cos x, e^x^ and ln x.
  • Apply the chain rule and write and use tangent lines.

Lessons

  1. The derivative as a limit 5 steps3 practiceabout 30 min
  2. Graphs of f and f′ 5 steps4 practiceabout 30 min
  3. The power rule and its companions 5 steps3 practiceabout 30 min
  4. Products, quotients and transcendental functions 5 steps3 practiceabout 32 min
  5. The chain rule and tangent lines 6 steps3 practiceabout 33 min
  6. Derivatives check 12 questions at the end

Keep exploring

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Guide for grown-ups