#### Chapters

## Chapter 9: Differentiation

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

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

x^{12}

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

x^{–9}

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

`x^(3/2)`

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

`7xsqrt x`

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

3^{5}

Differentiate the following w. r. t. x.: x^{5 }+ 3x^{4}

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

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

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

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

Differentiate the following w. r. t. x. : x^{3} log x

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

Differentiate the following w. r. t. x. : e^{x} log x

Differentiate the following w. r. t. x. : x^{3} .3^{x}

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

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

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

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

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

Find the derivative of the following function by the first principle: 3x^{2 }+ 4

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

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

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

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

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

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

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

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

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

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

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

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

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/-.

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

The demand function of a commodity is given as P = 20 + D − D^{2}. Find the rate at which price is changing when demand is 3.

Solve the following example: If the total cost function is given by; C = 5x^{3} + 2x^{2} + 7; find the average cost and the marginal cost when x = 4.

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

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

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.

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

Solve the following example: The demand function is given as P = 175 + 9D + 25D^{2} . Find the revenue, average revenue, and marginal revenue when demand is 10.

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

The cost of producing x articles is given by C = x^{2} + 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.

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

Differentiate the following function .w.r.t.x. : x^{5}

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

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

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

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

Differentiate the followingfunctions.w.r.t.x. : 7^{x}

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

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

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

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

Find `dy/dx` if y = x^{2} + 2^{x} – 1

Find `dy/dx` if y = (1 – x) (2 – x)

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

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

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

Find `dy/dx`if y = x log x (x^{2} + 1)

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.

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

The supply S of electric bulbs at price P is given by S = 2P^{3} + 5. Find the marginal supply when the price is ₹ 5/- Interpret the result.

The marginal cost of producing x items is given by C = x^{2} + 4x + 4. Find the average cost and the marginal cost. What is the marginal cost when x = 7.

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/-.

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

The demand function of a commodity is given as P = 20 + D − D^{2}. Find the rate at which price is changing when demand is 3.

If the total cost function is given by C = 5x^{3} + 2x^{2} + 1; Find the average cost and the marginal cost when x = 4.

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

The cost of producing x articles is given by C = x^{2} + 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

## 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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