RD Sharma Class 12 Solutions Chapter 11 - Differentiation (Ex 11.3) Exercise 11.3

Differentiation is called to be a process of finding the derivatives for a function. In calculus. A derivative is defined as the rate of change for a function in respect to another quantity. So in easy words differentiation is the rate of change with respect to 2 two different quantities.

Differentiation mainly calculates the ratio of small 3 which occurs in one particular quantity with respect to the small changes that occur in another quantity, keeping in mind that these two quantities under observation are dependent on each other.

As we have established that differentiation concerns derivatives, so the three main derivatives in concern are as follows:

1.    algebraic functions, D(xn) = nxn − 1, n is any real number;

2.   trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and

3.   exponential function, D(ex) = ex.

There are various techniques which are used for the Differentiation of Calculus such as

• The product rule
• The quotient rule
• The chain rule
• This particular chain rule is classified as a general power rule, and general exponential rule and the general logarithm rule.

Few common properties of the derivatives are as follows

• The situation where the limit of a sum is the sum of the limits
• The situation where the limit of a product is the product of the limit.

Outline for R D Sharma Chapter 11 Class 12th :

• Exercise 11.1- 10 question
• Exercise 11.2- 74 question
• Exercise 11.3- 48 question
• Exercise 11.4- 30 question
• Exercise 11.5- 69 question
• Exercise 11.6- 8 question
• Exercise 11.7- 28 question
• Exercise 11.8- 24 question
• Exercise 11 MCQ- 17 question
• Exercise 11 V S A Q- 16 question