Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 56

EASY

NDA & NA EE

IMPORTANT

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If $y = \frac{x + 1}{x - 1}$ , then what is the value of $\frac{d y}{d x} ?$

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Important Questions on Differentiation

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 57

What is the rate of change of

\sqrt{x^{2} + 16}

w.r.t.,

x^{2}

at

x = 3 ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 58

If

y = \cos t

and

x = \sin t

, then what is the value of

\frac{d y}{d x} ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 59

If

f (x) = 2^{\sin x}

, then what is the derivative of

f (x) ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 60

If

y = In (e^{m x} + e^{- m x})

, then what is the value of

\frac{d y}{d x}

at

x = 0 ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 61

If

x^{m} + y^{m} = 1

, such that

\frac{d y}{d x} = - \frac{x}{y}

, then what should be the value of

m ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 62

Consider the following statements:

$I .$ If $y = \ln (\sec x + \tan x)$ , then $\frac{d y}{d x} = \sec x$

$II .$ If $y = \ln (cosec x - \cot x)$ , then $\frac{d y}{d x} = cosec x$

Which of the above statement(s) is/are correct?

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 63

The derivative of

\sec^{2} x

w.r.t.

\tan^{2} x

is

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 64

If

y = \sin (a x + b)

, then what is

\frac{d^{2} y}{d x^{2}}

at

x = - \frac{b}{a}

, where

a

and

b

are constants and

a \neq 0 ?