# Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 9 - Differentiation [Latest edition]

## Chapter 9: Differentiation

Exercise 9.1Exercise 9.2Miscellaneous Exercise 9
Exercise 9.1 [Page 120]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 9 Differentiation Exercise 9.1 [Page 120]

Exercise 9.1 | Q I. (1) | Page 120

Find the derivative of the following function w.r.t. x:

x12

Exercise 9.1 | Q I. (2) | Page 120

Find the derivative of the following function w.r.t. x.:

x–9

Exercise 9.1 | Q I. (3) | Page 120

Find the derivative of the following functions w. r. t. x.:

x^(3/2)

Exercise 9.1 | Q I. (4) | Page 120

Find the derivative of the following function w. r. t. x.:

7xsqrt x

Exercise 9.1 | Q I. (5) | Page 120

Find the derivative of the following function w. r. t. x.:

35

Exercise 9.1 | Q II. (1) | Page 120

Differentiate the following w. r. t. x.: x5 + 3x4

Exercise 9.1 | Q II. (2) | Page 120

Differentiate the following w. r. t. x. : x sqrtx + logx − e^x

Exercise 9.1 | Q II. (3) | Page 120

Differentiate the following w. r. t. x. : x^(5/2) + 5x^(7/5)

Exercise 9.1 | Q II. (4) | Page 120

Differentiate the following w. r. t. x. : 2/7 x^(7/2) + 5/2 x^(2/5)

Exercise 9.1 | Q II. (5) | Page 120

Differentiate the following w. r. t. x. : sqrtx (x^2 + 1)^2

Exercise 9.1 | Q III. (1) | Page 120

Differentiate the following w. r. t. x. : x3 log x

Exercise 9.1 | Q III. (2) | Page 120

Differentiate the following w. r. t. x. : x^(5/2) e^x

Exercise 9.1 | Q III. (3) | Page 120

Differentiate the following w. r. t. x. : ex log x

Exercise 9.1 | Q III. (4) | Page 120

Differentiate the following w. r. t. x. : x3 .3x

Exercise 9.1 | Q IV. (1) | Page 120

Find the derivative of the following w. r. t.x. : (x^2+a^2)/(x^2-a^2)

Exercise 9.1 | Q IV. (2) | Page 120

Find the derivative of the following w. r. t.x. : (3x^2+5)/(2x^2-4)

Exercise 9.1 | Q IV. (3) | Page 120

Find the derivative of the following w. r. t. x. : logx/(x^3-5)

Exercise 9.1 | Q IV. (4) | Page 120

Find the derivative of the following w. r. t.x. : (3e^x-2)/(3e^x+2)

Exercise 9.1 | Q IV. (5) | Page 120

Find the derivative of the following w. r. t. x. : (xe^x)/(x+e^x)

Exercise 9.1 | Q V. (1) | Page 120

Find the derivative of the following function by the first principle: 3x2 + 4

Exercise 9.1 | Q V. (2) | Page 120

Find the derivative of the following function by the first principle: x sqrtx

Exercise 9.1 | Q V. (3) | Page 120

Find the derivative of the following functions by the first principle: 1/(2x + 3)

Exercise 9.1 | Q V. (4) | Page 120

Find the derivative of the following function by the first principle: (x - 1)/(2x + 7)

Exercise 9.2 [Pages 122 - 123]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 9 Differentiation Exercise 9.2 [Pages 122 - 123]

Exercise 9.2 | Q I. (1) | Page 122

Differentiate the following function w.r.t.x. : x/(x + 1)

Exercise 9.2 | Q I. (2) | Page 122

Differentiate the following function w.r.t.x : (x^2 + 1)/x

Exercise 9.2 | Q I. (3) | Page 122

Differentiate the following function w.r.t.x. : 1/("e"^x + 1)

Exercise 9.2 | Q I. (4) | Page 122

Differentiate the following function w.r.t.x. : "e"^x/("e"^x + 1)

Exercise 9.2 | Q I. (5) | Page 122

Differentiate the following function w.r.t.x. : x/log x

Exercise 9.2 | Q I. (6) | Page 122

Differentiate the following function w.r.t.x. : 2^x/logx

Exercise 9.2 | Q I. (7) | Page 122

Differentiate the following function w.r.t.x. : ((2"e"^x - 1))/((2"e"^x + 1))

Exercise 9.2 | Q I. (8) | Page 122

Differentiate the following function w.r.t.x. : ((x+1)(x-1))/(("e"^x+1))

Exercise 9.2 | Q II. (1) | Page 122

The demand D for a price P is given as D = 27/"P", find the rate of change of demand when price is Rs. 3/-.

Exercise 9.2 | Q II. (2) | Page 122

If for a commodity; the price-demand relation is given as D =("P"+ 5)/("P" - 1). Find the marginal demand when price is 2.

Exercise 9.2 | Q II. (3) | Page 122

The demand function of a commodity is given as P = 20 + D − D2. Find the rate at which price is changing when demand is 3.

Exercise 9.2 | Q II. (4) | Page 122

Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.

Exercise 9.2 | Q II. (5) | Page 122

Solve the following example: The total cost function of producing n notebooks is given by C= 1500 − 75n + 2n2 + "n"^3/5. Find the marginal cost at n = 10.

Exercise 9.2 | Q II. (6) | Page 123

Solve the following example: The total cost of ‘t’ toy cars is given by C=5(2t)+17. Find the marginal cost and average cost at t = 3.

Exercise 9.2 | Q II. (7) | Page 123

Solve the following example: If for a commodity; the demand function is given by, D = sqrt(75 − 3"P"). Find the marginal demand function when P = 5.

Exercise 9.2 | Q II. (8) | Page 123

Solve the following example: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.

Exercise 9.2 | Q II. (9) | Page 123

Solve the following example: The demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.

Exercise 9.2 | Q II. (10) | Page 123

The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.

Exercise 9.2 | Q II. (11) | Page 123

The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.

Miscellaneous Exercise 9 [Pages 123 - 124]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 9 Differentiation Miscellaneous Exercise 9 [Pages 123 - 124]

Miscellaneous Exercise 9 | Q I. (1) | Page 123

Differentiate the following function .w.r.t.x. : x5

Miscellaneous Exercise 9 | Q I. (2) | Page 123

Differentiate the following function w.r.t.x. : x−2

Miscellaneous Exercise 9 | Q I. (3) | Page 123

Differentiate the following functions w.r.t.x. :sqrtx

Miscellaneous Exercise 9 | Q I. (4) | Page 123

Differentiate the following function w.r.t.x. : xsqrt x

Miscellaneous Exercise 9 | Q I. (5) | Page 123

Differentiate the followingfunctions.w.r.t.x.: 1/sqrtx

Miscellaneous Exercise 9 | Q I. (6) | Page 123

Differentiate the followingfunctions.w.r.t.x. : 7x

Miscellaneous Exercise 9 | Q II. (1) | Page 123

Find dy/dx if y = x^2 + 1/x^2

Miscellaneous Exercise 9 | Q II. (2) | Page 123

Find dy/dx if y=(sqrtx+1)^2

Miscellaneous Exercise 9 | Q II. (3) | Page 123

Find dy/dx if y = (sqrtx + 1/sqrtx)^2

Miscellaneous Exercise 9 | Q II. (4) | Page 123

Find dy/dx if y = x^3 – 2x^2 + sqrtx + 1

Miscellaneous Exercise 9 | Q II. (5) | Page 123

Find dy/dx if y = x2 + 2x – 1

Miscellaneous Exercise 9 | Q II. (6) | Page 123

Find dy/dx if y = (1 – x) (2 – x)

Miscellaneous Exercise 9 | Q II. (7) | Page 123

Find dy/dx if y=(1+x)/(2+x)

Miscellaneous Exercise 9 | Q II. (8) | Page 123

Find dy/dx if y = ((logx+1))/x

Miscellaneous Exercise 9 | Q II. (9) | Page 123

Find dy/dx if y = "e"^x/logx

Miscellaneous Exercise 9 | Q II. (10) | Page 123

Find dy/dxif y = x log x (x2 + 1)

Miscellaneous Exercise 9 | Q III. (1) | Page 124

The relation between price (P) and demand (D) of a cup of Tea is given by D = 12/"P". Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result.

Miscellaneous Exercise 9 | Q III. (2) | Page 124

The demand (D) of biscuits at price P is given by D = 64/"P"^3, find the marginal demand when price is Rs. 4/-.

Miscellaneous Exercise 9 | Q III. (3) | Page 124

The supply S of electric bulbs at price P is given by S = 2P3 + 5. Find the marginal supply when the price is ₹ 5/- Interpret the result.

Miscellaneous Exercise 9 | Q III. (4) | Page 124

The marginal cost of producing x items is given by C = x2 + 4x + 4. Find the average cost and the marginal cost. What is the marginal cost when x = 7.

Miscellaneous Exercise 9 | Q III. (5) | Page 124

The demand D for a price P is given as D = 27/"P", find the rate of change of demand when price is Rs. 3/-.

Miscellaneous Exercise 9 | Q III. (6) | Page 124

If for a commodity; the price-demand relation is given as D =("P"+ 5)/("P" - 1). Find the marginal demand when price is 2.

Miscellaneous Exercise 9 | Q III. (7) | Page 124

The demand function of a commodity is given as P = 20 + D − D2. Find the rate at which price is changing when demand is 3.

Miscellaneous Exercise 9 | Q III. (8) | Page 124

If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.

Miscellaneous Exercise 9 | Q III. (9) | Page 124

The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.

Miscellaneous Exercise 9 | Q III. (10) | Page 124

The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.

## Chapter 9: Differentiation

Exercise 9.1Exercise 9.2Miscellaneous Exercise 9

## Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 9 - Differentiation

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 9 (Differentiation) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 9 Differentiation are The Meaning of Rate of Change, Definition of Derivative and Differentiability, Derivative by the Method of First Principle, Rules of Differentiation (Without Proof), Applications of Derivatives.

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