#### Online Mock Tests

#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## Chapter 2: Differentiation

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Differentiation MCQ

#### 2 Marks each

If y = sec (tan^{−1}x) then `("d"y)/("d"x)` at x = 1 is ______

`1/2`

1

`1/sqrt(2)`

`sqrt(2)`

If f(x) = log_{x} (log x) then f'(e) is ______

1

e

`1/"e"`

0

If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______

1

0

9

cos x – sin x

If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______

35

12

`7/5`

105

If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (1, 1) then `("d"y)/("d"x)` = ______

`(-2)/(1 + x^2)`

1

`(2)/(1 + x^2)`

`1/(1 + x^2)`

If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(x) = ______

`1/(1 + ["g"(x)]^4`

`(4x^3)/(1 + x^4)`

`1/(1 + ["g"(x)]^3`

`1 + ["g"(x)]^4`

If sin^{−1}(x^{3} + y^{3}) = a then `("d"y)/("d"x)` = ______

`(-x)/(cos"a")`

`(-x^2)/(y^2)`

`(y^2)/(x^2)`

`sin"a"/y`

If x = cos^{−1}(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______

t

– t

`(-1)/"t"`

`1/"t"`

If x^{2} + y^{2} = 1 then `("d"^2x)/("d"y^2)` = ______

x

^{3}y

^{3}– y

^{3}`(-1)/x^3`

If x^{2} + y^{2} = t + `1/"t"` and x^{4} + y^{4} = t^{2} + `1/"t"^2` then `("d"y)/("d"x)` = ______

`x/(2y)`

`(-y)/x`

`(-x)/(2y)`

`y/x`

If x = a t^{4} y = 2a t^{2} then `("d"y)/("d"x)` = ______

`1/"t"`

`(-1)/"t"`

`1/"t"^2`

`(-1)/"t"^2`

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Differentiation Very Short Answers

#### 1 Mark each

Differentiate y = `sqrt(x^2 + 5)` w.r. to x

Differentiate y = e^{tanx} w.r. to x

If y = sin^{−1} (2^{x}), find `("d"y)/(""d"x)`

If f(x) is odd and differentiable, then f′(x) is

If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Differentiation Short Answers I

#### 2 mark each

If y = log [cos(x^{5})] then find `("d"y)/("d"x)`

If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`

Find the derivative of the inverse of function y = 2x^{3} – 6x and calculate its value at x = −2

Let f(x) = x^{5} + 2x – 3 find (f^{−1})'(-3)

If y = cos^{−1} [sin (4^{x})], find `("d"y)/("d"x)`

If y = `tan^-1[sqrt(1 + cos x)/(1 - cos x)]`, find `("d"y)/("d"x)`

If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`

Differentiate sin^{2} (sin^{−1}(x^{2})) w.r. to x

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Differentiation Short Answers II

#### 3 marks each

If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`

If y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`, find `("d"y)/("d"x)`

Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x

Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x

Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x

If log_{5} `((x^4 + y^4)/(x^4 - y^4))` = 2, show that `("d"y)/("d"x) = (12x^2)/(13y^3)`

If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`

Find the derivative of cos^{−1}x w.r. to `sqrt(1 - x^2)`

If x sin(a + y) + sin a cos(a + y) = 0 then show that `("d"y)/("d"x) = (sin^2("a" + y))/(sin"a")`

If y = 5^{x}. x^{5}. x^{x}. 5^{5} , find `("d"y)/("d"x)`

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Differentiation Long Answers III

#### 4 Marks each

If y = `"e"^("m"tan^(-1)x`, show that `(1 + x^2) ("d"^2y)/("d"x^2) + (2x - "m")("d"y)/("d"x)` = 0

If x^{7} . y^{5} = (x + y)^{12}, show that `("d"y)/("d"x) = y/x`

Differentiate `tan^-1[(sqrt(1 + x^2) - 1)/x]` w.r. to `tan^-1[(2x sqrt(1 - x^2))/(1 - 2x^2)]`

If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`

If y = cos(m cos^{–1}x), then show that `(1 - x^2) ("d"^2y)/("d"x^2) - x("d"y)/("d"x) + "m"^2y` = 0

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Differentiation :: Theorems ::

If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x such that the composite function y = f[g(x)] is a differentiable function of x, then `("d"y)/("d"x) = ("d"y)/("d"u)*("d"u)/("d"x)`. Hence find `("d"y)/("d"x)` if y = sin^{2}x

Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f^{–1}(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0

If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable function of x and it `("d"x)/("dt")` ≠ 0 then `("d"y)/("d"x) = (("d"y)/("dt"))/(("d"x)/("dt"))`

## Chapter 2: Differentiation

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 - Differentiation

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 (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 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 Differentiation are Differentiation, Derivatives of Composite Functions - Chain Rule, Geometrical Meaning of Derivative, Derivatives of Inverse Functions, Logarithmic Differentiation, Derivatives of Implicit Functions, Derivatives of Parametric Functions, Higher Order Derivatives.

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