OP Malhotra Class-11 Differentiation S.Chand ISC Maths Solution

OP Malhotra Class-11 Differentiation S.Chand ISC Maths Solution Chapter-19. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-19 (a), 19 (b), 19 (c), 19 (d), With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Class-11 Differentiation S.Chand ISC Maths Solution

Class:	11th
Subject:	Mathematics
Chapter  :	Ch-19 Differentiation of Section -A

Board	ISC
Writer	OP Malhotra
Publications	S.Chand Publications 2020-21

---

–: Select Topics :-

Exe-19 (a)

Exe-19 (b)

Exe-19 (c)

Exe-19 (d)

Chapter Test

---

OP Malhotra Class-11 Differentiation S.Chand ISC Maths Solution

Differentiation in Maths:

In Mathematics, Differentiation can be defined as a derivative of a function with respect to an independent variable. Differentiation, in calculus, can be applied to measure the function per unit change in the independent variable.

Derivative of Function As Limits

If we are given with real valued function (f) and x is a point in its domain of definition, then the derivative of function, f, is given by:

f'(a) = lim_h→0[f(x+h)-f(x)]/h

provided this limit exists.

Notations

When a function is denoted as y=f(x), the derivative is indicated by the following notations.

1. D(y) or D[f(x)] is called Euler’s notation.
2. dy/dx is called Leibniz’s notation.
3. F’(x) is called Lagrange’s notation.

The meaning of differentiation is the process of determining the derivative of a function at any point.

Linear and Non-Linear Functions

Functions are generally classified in two categories under Calculus, namely:

(i) Linear functions

(ii) Non-linear functions

A linear function varies with a constant rate through its domain. Therefore, the overall rate of change of the function is the same as the rate of change of a function at any point.

However, the rate of change of function varies from point to point in case of non-linear functions. The nature of variation is based on the nature of the function.

The rate of change of a function at a particular point is defined as a derivative of that particular function.

Differentiation Rules

The basic differentiation rules that need to be followed are as follows:

• Sum and Difference Rule
• Product Rule
• Quotient Rule
• Chain Rule

Let us discuss here.

Sum or Difference Rule

If the function is sum or difference of two functions, the derivative of the functions is the sum or difference of the individual functions, i.e.,

If f(x) = u(x) ± v(x)

then, f'(x)=u'(x) ± v'(x)

Product Rule

As per the product rule, if the function f(x) is product of two functions u(x) and v(x), the derivative of the function is,

If f(x)=u(x)×v(x)

then, f′(x)=u′(x)×v(x)+u(x)×v′(x)

---