1. MATH 31 LESSONS Chapters 6 & 7: Trigonometry 9. Derivatives of Other Trig Functions

2. Section 7.3: Derivatives of Other Trigonometric Functions Read Textbook pp. 315 - 319

3. Derivatives of Other Trig Functions We will now look at the derivatives of other trig functions. Each of these formulas are derived from the derivatives of sine / cosine, as will be shown in the first example.

4. Formulas:

5. Note: If the trig functions have an “inside function u(x)”, then the formulas can be altered as follows:

6. Ex. 1Prove that Try this example on your own first. Then, check out the solution.

7. Reduce the trig function to sine and cosine.

8. Quotient Rule:

10. Simplify and factor out the negative from the numerator.

12. Ex. 2Differentiate. Try this example on your own first. Then, check out the solution.

13. If it helps, substitute u(x) for the “inside function”

14. Find the derivative of the “outside function”. Leave the inside function the same. Don’t forget to find the derivative of the “inside function”

15. Back substitute.

17. Ex. 3Differentiate. Try this example on your own first. Then, check out the solution.

18. Remember, the entire tangent function is being squared. i.e. tan 2 x = (tan x) 2

19. Find the derivative of the “outside function”. Leave the inside function the same. Don’t forget to find the derivative of the “inside function” Chain rule

20. Chain rule again.

22. Ex. 4Differentiate. Try this example on your own first. Then, check out the solution.

23. First, write in exponential notation.

24. Find the derivative of the “outside function”. Leave the inside function the same. Don’t forget to find the derivative of the “inside function” Chain rule

25. Chain rule again.

27. Bring all the coefficients together

29. Notice, u  3/2  u 1 = u  1/2