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BENNY VARGHESE,

PGT Mathematics,

Jawahar Navodaya Vidyalaya,

PATHANAMTHITTA

KERALA-686511

Ch 5 >> CONTINUITY AND DIFFERENTIABILITY

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DERIVATIVES

Derivatives are met in many engineering and science problems, especially when modelling the behaviour of moving objects.

We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).

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After studying this lesson, you will be able to :

 

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  • state and apply the chain rule for the derivative of a function;

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  • find the derivative of algebraic functions (including rational functions); and

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  • find second order derivative of a function.

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Differentiability at a point.

 

 

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Geometrical meaning:

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Derivative of a function:

 

This definition of derivative is also called the first principle of derivative.

 

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Theorem:

 

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Derivative of some standard functions:

 

 

 

 

 

 

 

 

 

 

 

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Theorem:

 

 

 

 

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DIFFERENTIATION OF A FUNCTION OF A FUNCTION

Chain Rule for Differentiation:

 

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Remark 1

 

Remark 2

 

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ALITER

 

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Thank you