Derivatives: The Formal Definition


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Where t= time, what is the derivative of f(t)?

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Which of the following best describe(s) the derivative of a function?

a) It is the instantaneous rate of change.

b) It is the slope between any two points.

c) It is the tangent to the function.


Which of the following statements are true?

a) d/dx f(x) = f'(x)

b) f'(x) is the derivative of the function f(x) with respect to x.

c) d/dx f(x) describes the instantaneous rate of change of f(x).

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About This Quiz & Worksheet

The derivative, or instantaneous rate of change, is essential to calculus. This quiz and worksheet combination will help test your knowledge of derivatives, including formula calculations and practical application.

Quiz & Worksheet Goals

This assessment will test your knowledge in the following areas:

  • Practical application of derivatives
  • Definition of key terms

Skills Practiced

  • Critical thinking - apply relevant concepts to examine information about derivatives in a different light
  • Problem solving - use acquired knowledge to solve practice problems containing derivatives
  • Interpreting information - verify that you can read information regarding derivatives and interpret it correctly

Additional Learning

The lesson Derivatives: The Formal Definition, along with this quiz and worksheet, contains the following objectives:

  • Describe multiple ways to denote derivatives
  • Determine begin time and end time when calculating formula