RS Aggarwal Class 11 Chapter 28 Solutions (Differentiation)

RS Aggarwal Class 11 Solutions for Chapter 28 is the next tricky Chapter of the same level after Chapter 27 Limits. RS Aggarwal Solutions prepared by our experts makes the difficulty level of this Chapter easy for you, simplified methods to solve the answers. RS Aggarwal Solutions give you all the possible ways, methods and formulas used to solve the question and you can choose the one you find easy.

The Chapter has 5 exercises with 57 questions and many solved examples in total. The Solutions by RS Aggarwal contains all the necessary topics which are there in the Chapter with easy concepts. By just practising all the questions and solved examples by RS Aggarwal you can score better in the CBSE exams. The presentation of the Solutions by our experts is done in a way that makes it easy for you to learn even the difficult topic easily.

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Important points of the Chapter Differentiation

  • The method of finding the derivative of a function is known as Differentiation.
  • Differentiation can also be said as the method of finding the instantaneous rate of change in a function based on one of its variables.
  • If the derivative f'(a) exists at every point in its domain, A function f in x is said to be differentiable at the point x = a.
  • If x and y are given as variables, then the rate of change of x with respect to y would be dy/dx.
  • There are 2 types of functions under Calculus – Linear, and Nonlinear.
  • A linear function is a function that varies with a constant rate through its domain.
  • In a nonlinear function, the rate of change of the function varies from one point to the other point.
  • A derivative is known as the rate of change of a given function at a specific point.
  • According to the chain rule of differentiation, 

If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx

  • If y = f(x) is a function of x, then the rate of change of “y” per unit change in “x” is given by – dy/dx.
  • dy/dx is called Leibniz’s notation
  • Differentiation can also be known as the process of determining the derivative of a function at a point.

Topics Covered Under Chapter 28 Differentiation 

  • 2 types of functions
  • Differentiation in calculus
  • Differentiation formulas
  • Differentiation rules
  1. The sum or difference rule
  2. Product rule
  3. Quotient rule
  4. Chain rule
  • Algebra of differentiation

Important Differentiation Formulas used in the Chapter

  1. If f(x) = tan (x), then f’(x) = sec²x
  2. If f(x) = cos (x), then f’(x) = -sinx
  3. If f(x) = sin (x), then f’(x) = cosx
  4. If f(x) = In(x), then f’(x) = 1/x
  5. If f(x) = k, where k is given as a constant, then f’(x) = 0

Exercise Wise Discussion of RS Aggarwal Class 11 Chapter 28 Differentiation

Exercise 28A

This exercise 28A has 6 questions in which you have to:

  • Differentiate the given functions

Exercise 28B

This exercise 28B has 12 questions in which you have to:

  • Find the derivation of the given derivative using the first principle.

Exercise 28C

This exercise 28C has 7 questions in which you have to:

  • Differentiate the given functions using the product rule.

Exercise 28D

This exercise 28D has 12 questions in which you have to:

  • Differentiate the given functions using the quotient rule.

Exercise 28E

This exercise 28E has 20  questions in which you have to:

  • Differentiate the given functions with respect to x, using the chain rule.

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