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

Implicit function differentiation

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

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

Example: Solution: differentiate both sides with respect to x

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

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

Thanks Radia