text: # In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
  
  ## Presentation on theme: "In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules."— Presentation transcript:
  
  In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
  
  Let f be any function. The derivative function of f is defined as: provided the limit exists Other notations:
  
  Use the definition of derivative to find the derivative of the function.
  
  Let n be any real number (not necessarily an integer). Then:
  
  Find the derivative of each of the following functions. (a) (b) (c)
  
  Let f be any differentiable function, let k be any constant, and let. Then:
  
  Let f and g be any differentiable functions, and let. Then:
  
  Find the derivative of each of the following polynomials. (a) (b) (c)
  
  Give the equation of the tangent line to the curve at the point (1, 3).
  
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explanation: The document is a presentation transcript or notes on the topic of derivatives in calculus. It covers the definition of the derivative function, basic derivative rules, and examples of finding derivatives of functions. The document contains several questions and answers related to finding derivatives and the equation of a tangent line.
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distilabel_metadata.content: # In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
  
  ## Presentation on theme: "In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules."— Presentation transcript:
  
  In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
  
  Let f be any function. The derivative function of f is defined as: provided the limit exists Other notations:
  
  Use the definition of derivative to find the derivative of the function.
  
  Let n be any real number (not necessarily an integer). Then:
  
  Find the derivative of each of the following functions. (a) (b) (c)
  
  Let f be any differentiable function, let k be any constant, and let. Then:
  
  Let f and g be any differentiable functions, and let. Then:
  
  Find the derivative of each of the following polynomials. (a) (b) (c)
  
  Give the equation of the tangent line to the curve at the point (1, 3).
  
  Download ppt "In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules."
  
  Similar presentations
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distilabel_metadata.raw_output_q_a_detector_0: The document is a presentation transcript or notes on the topic of derivatives in calculus. It covers the definition of the derivative function, basic derivative rules, and examples of finding derivatives of functions. The document contains several questions and answers related to finding derivatives and the equation of a tangent line.
  
  Label: multiple-question-and-answer