1. Umm Al-Qura University
بسم الله الرحمن الرحيم
Umm Al-Qura University
Health Sciences College at Al-Leith
Department of Public Health
Lecture (8)

2. differentiation of Inverse Trigonometric functions

3. Objectives:
1/ Show the table of differentiation of Inverse Trigonometric functions.
2/ Apply differentiation of Inverse Trigonometric functions by using General Low.

4. we have

7. Summary
Derivative
Function
sin-1x
cos-1x
tan-1x
cot-1x
sec-1x
csc-1x

8. Find dy/dx if y = x2 tan-1x Solution : dy/dx = x2 + tan-1x (2x)
Example
Find dy/dx if y = x2 tan-1x
Solution :
dy/dx = x tan-1x (2x)
= x x tan-1x

9. Find dy/dx if y = x sin-1x Solution : dy/dx = x + sin-1x (1)
Example
Find dy/dx if y = x sin-1x
Solution :
dy/dx = x sin-1x (1)
= x sin-1x

10. Find dy/dx if y = sinx tan-1x Solution : dy/dx = sinx + tan-1x (cosx)
Example
Find dy/dx if y = sinx tan-1x
Solution :
dy/dx = sinx tan-1x (cosx)
= sinx cosx tan-1x

11. Find dy/dx if y = 3x sec-1x Solution : dy/dx = 3x + sec-1x (3)
Example
Find dy/dx if y = 3x sec-1x
Solution :
dy/dx = 3x sec-1x (3)
= 3x sec-1x

12. b. y = sin-1x . tan-1x C. y = x ln(x) + 5cot-1x
Exercise
Find dy/dx for the following functions
a. y = cos-1x / ex
b. y = sin-1x . tan-1x
C. y = x ln(x) + 5cot-1x

13. Thanks Radia