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

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Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 9 - Differentiation - Shaalaa.com
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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/dx`if 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.

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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 - Shaalaa.com

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.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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.

Using Balbharati 11th solutions Differentiation exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 11th prefer Balbharati Textbook Solutions to score more in exam.

Get the free view of chapter 9 Differentiation 11th extra questions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation

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