### 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 .

• PROBLEM 2 : Differentiate .

• PROBLEM 3 : Differentiate .

• PROBLEM 4 : Differentiate .

• PROBLEM 5 : Differentiate .

• PROBLEM 6 : Differentiate .

• PROBLEM 7 : Differentiate .

• PROBLEM 8 : Evaluate .

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

• PROBLEM 9 : Differentiate .

• PROBLEM 10 : Differentiate .

• PROBLEM 11 : Differentiate .

• PROBLEM 12 : Differentiate .

• PROBLEM 13 : Differentiate .

• PROBLEM 14 : Differentiate .

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

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

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

• PROBLEM 18 : Use any method to verify that .