Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 82

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IMPORTANT

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If $y = \cot^{- 1} [\frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}}]$ , where $0 < x < \frac{π}{2}$ , then $\frac{d y}{d x}$ is equal to

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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 1

If

y = \sec (\tan^{- 1} x)

, then

\frac{d y}{d x}

is equal to

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 2

If

y = \tan^{- 1} (\frac{\sin x}{1 + \cos x})

, then

\frac{d y}{d x}

is equal to

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 3

If

y = {\{x + \sqrt{1 + x^{2}}\}}^{m}

, then

(1 + x^{2}) y_{2} + x y_{1} - m^{2} y

is equal to

HARD

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 4

If

f (x) = \log_{a} (\log_{a} x)

, then

f^{'} (x)

is equal to

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 5

If

x = a (1 - \cos θ), y = a (θ - \sin θ)

, then

{(\frac{d y}{d x})}_{θ = \frac{π}{2}}

is equal to

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 6

The derivative of the function

\cot^{- 1} [{(\cos 2 x)}^{\frac{1}{2}}]

at

x = \frac{π}{6}

is

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 7

If

y = \tan^{- 1} [\frac{\{\sqrt{(1 + x^{2})} - 1\}}{x}]

, then

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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 8

If

y = \sin^{- 1} \frac{\sqrt{(1 + x)} + \sqrt{(1 - x)}}{2}

, then

\frac{d y}{d x}

is equal to