DIFFERENTIATION OF TRIGONOMETRY FUNCTIONS

In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x) . The following problems require the use of these six basic trigonometry derivatives :

1. 
2. 
3. 
4. 
5. 
6. 

These rules follow from the limit definition of derivative, special limits, trigonometry identities, or the quotient rule. In the list of problems which follows, most problems are average and a few are somewhat challenging.

On problems 1.) through 8.) find answers WITHOUT using the chain rule.

• PROBLEM 1 : Differentiate .

  Click HERE to see a detailed solution to problem 1.
  
  
  

• PROBLEM 2 : Differentiate .

  Click HERE to see a detailed solution to problem 2.
  
  
  

• PROBLEM 3 : Differentiate .

  Click HERE to see a detailed solution to problem 3.
  
  
  

• PROBLEM 4 : Differentiate .

  Click HERE to see a detailed solution to problem 4.
  
  
  

• PROBLEM 5 : Differentiate .

  Click HERE to see a detailed solution to problem 5.
  
  
  

• PROBLEM 6 : Differentiate .

  Click HERE to see a detailed solution to problem 6.
  
  
  

• PROBLEM 7 : Differentiate .

  Click HERE to see a detailed solution to problem 7.
  
  
  

• PROBLEM 8 : Evaluate .

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Some of the following problems require use of the chain rule.

• PROBLEM 9 : Differentiate .

  Click HERE to see a detailed solution to problem 9.
  
  
  

• PROBLEM 10 : Differentiate .

  Click HERE to see a detailed solution to problem 10.
  
  
  

• PROBLEM 11 : Differentiate .

  Click HERE to see a detailed solution to problem 11.
  
  
  

• PROBLEM 12 : Differentiate .

  Click HERE to see a detailed solution to problem 12.
  
  
  

• PROBLEM 13 : Differentiate .

  Click HERE to see a detailed solution to problem 13.
  
  
  

• PROBLEM 14 : Differentiate .

  Click HERE to see a detailed solution to problem 14.
  
  
  

• PROBLEM 15 : Find an equation of the line tangent to the graph of at x=-1 .

  Click HERE to see a detailed solution to problem 15.
  
  
  

• PROBLEM 16 : Find an equation of the line perpendicular to the graph of at .

  Click HERE to see a detailed solution to problem 16.
  
  
  

• PROBLEM 17 : Assume that . Solve f'(x) = 0 for x in the interval .

  Click HERE to see a detailed solution to problem 17.
  
  
  

• PROBLEM 18 : Use any method to verify that .

  Click HERE to see a detailed solution to problem 18.
  
  
  

Click HERE to return to the original list of various types of calculus problems.

Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :

kouba@math.ucdavis.edu

 
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