1. Inverse Trigonometric Functions and Their Derivatives
                                                   
Inverse Trigonometric Functions and Their Derivatives

2. Not a one-to-one function

4. Find the exact value of
Find the exact value of

5. A one-to-one function
Not a one-to-one function

7. Find the exact value of
Find the exact value of

8. Not a one-to-one function

10. Find the exact value of
Find the exact value of

11. Not a one-to-one function

13. Find the exact value of
Find the exact value of

17. What is the reference angle?

21. Not a one-to-one function

23. Derivatives of Inverse Functions
General formula for all inverse functions
Derivatives of Inverse Trigonometric Functions – six formulas to know

24. At x = 2:
We can find the inverse function as follows:
To find the derivative of the inverse function:
Switch x and y.

25. Slopes are reciprocals.
At x = 2:
At x = 4:

26. Slopes are reciprocals.
Because x and y are reversed to find the inverse function, the following pattern always holds:
The derivative of
Derivative Formula for Inverses:
evaluated at
is equal to the reciprocal of
the derivative of
evaluated at

27. A typical problem using this formula might look like this:
Given:
Find:
Derivative Formula for Inverses:

28. We can use implicit differentiation to find:

29. We can use implicit differentiation to find:
But
so is positive.

30. We could use the same technique to find and. 1
sec d x dx -

31. It is also useful to know the following when using your
calculator:

33. Using the basic formula :

34. Using the basic formula :

35. Using the basic formula :

36. Using the basic formula :

37. What does this mean ???
It means that
is a constant .

39. YUCK!!