1. Umm Al-Qura University
بسم الله الرحمن الرحيم
Umm Al-Qura University
Health Sciences College at Al-Leith
Department of Public Health
Lecture (6)

2. Implicit function differentiation

3. Objectives: 1/ Show the table of Implicit functions differentiation.
2/ Define Implicit functions differentiation Low .
3/ Calculate Functions by using Implicit differentiation Low.

4. To differentiate a function of y we differentiate with respect to x and then multiply by dy/dx.
Example:
Solution:

6. Example:
Solution: differentiate both sides with respect to x

8. Cos y . y’ Sin y -Sin y . y’ Cos y Sec2 y . y’ Tan y -csc2 y . y’
Summary of implicit derivatives for trigonometric functions
Derivative
Function
Cos y . y’
Sin y
-Sin y . y’
Cos y
Sec2 y . y’
Tan y
-csc2 y . y’
Cot y
Sec y tan y . y’
Sec y
-Csc y cot y . y’
Csc y

9. 1. x + y 2. sinx + 7y 3. x siny 4. xy + tanx 5. x/y
Find the derivative of the following functions:
1. x + y
2. sinx + 7y
3. x siny
4. xy + tanx
5. x/y

10. Thanks Radia