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Mathematics · Grade 11

Implicit and Related-Rate Reasoning

Learners differentiate equations that do not give y explicitly, derive the derivatives of inverse functions such as ln x, arcsin x and arctan x, solve related-rate problems about sliding ladders, spreading ripples, filling tanks and lengthening shadows, and use local linear approximation and differentials to estimate values and measurement errors.

  • 4 lessons
  • About 145 minutes
  • Implicit and related rates check: 11 questions
  • Ways to answer: choose an answer, type a number, put in order, true or false and write a short answer
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What learners will discover

  • Differentiate implicitly and find slopes of tangent lines to curves defined by equations.
  • Find derivatives of inverse functions, including ln x, arcsin x and arctan x.
  • Set up and solve related-rate problems, differentiating before substituting.
  • Use local linear approximation and differentials to estimate values and propagated errors.

Lessons

  1. Implicit differentiation 5 steps3 practiceabout 34 min
  2. Derivatives of inverse functions 5 steps3 practiceabout 32 min
  3. Related rates 6 steps3 practiceabout 42 min
  4. Linear approximation and differentials 5 steps3 practiceabout 37 min
  5. Implicit and related rates check 11 questions at the end

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