CBSE Class 11-Mathematics: Mathematics Revision Sheet for Class 11 and Class 12 Physics (For CBSE, ICSE, IAS, NET, NRA 2023)

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April 9,2012

Differentiation

We have two quantities and such that where is some function of . We may be interested in finding followings things

1.

2. Maximum and Minimum values of y. It can be finding with the method of Maxima and Minima

Is the called the derivative of y w. r. t to

It is defined as

Some commonly known functions and their derivatives are:-

Some important and useful rules for finding derivatives of composite functions

1. where c is constant

2. where a and b are function of

3.

4.

5.

6.

Maximum and Minimum values of

Step 1:

Fine the derivative of

Step2:

Equate

Solve the equation to find out the values of

Step3:

Find the second derivative of and calculate the values of

for the values of from step 2

If then the value of x corresponds to mimina of y then then can be find out by putting this value of

If then the value of corresponds to maxima of then can be find out by putting this value of

Integration

It reads as integration of function f (x) w. r. t. x within the limits from x = a to x = b.

Integration of some important functions are

Useful rules for integration are