1 of 20

BENNY VARGHESE,

PGT Mathematics,

Jawahar Navodaya Vidyalaya,

PATHANAMTHITTA

KERALA-686511

CH5>> CONTINUITY AND DIFFERENTIABILITY

2 of 20

Differentiation of Implicit Functions:

 

 

3 of 20

 

 

4 of 20

LOGARITHMIC DIFFERENTIATION

 

 

 

5 of 20

 

 

 

 

6 of 20

Alternatively, we may write

 

Differentiating with respect to x, we get

 

 

7 of 20

 

 

 

Differentiating with respect to x

 

 

 

8 of 20

 

 

 

 

 

 

Differentiating both side with respect to x

 

9 of 20

 

 

 

 

Differentiating both side with respect to x

 

10 of 20

 

 

 

 

 

11 of 20

DIFFERENTIATION OF PARAMETRIC FUNCTIONS

 

 

 

12 of 20

DIFFERENTIATION OF A FUNCTION with respect to ANOTHER FUNCTION

 

 

13 of 20

Second Order Derivative

 

 

 

 

14 of 20

Second Order Derivative of Parametric functions

 

 

 

15 of 20

MEAN VALUE THEOREMS

ROLLE’S THEOREM

 

 

16 of 20

Geometrical Interpretation of Rolle’s Theorem

17 of 20

Verification

18 of 20

LAGRANGE’S MEAN VALUE THEOREM

 

 

19 of 20

Geometrical Interpretation

20 of 20

Thank you