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

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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 $a \neq 0 ?$

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Important Questions on Differentiation

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 65

If

y = x^{x}

, then what is the value of

\frac{d y}{d x}

at

x = 1 ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 66

If

2 x^{3} - 3 y^{2} = 7

, then what is

\frac{d y}{d x}

equal to (where,

y \neq 0

)

?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 67

What is the derivative of

\sin (\sin x) ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 68

What is the derivative of

x^{3}

w.r.t.

x^{2} ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 69

If

f (x) = 2 x^{2} + 3 x - 5

, then what is

f^{'} (0) + 3 f^{'} (- 1)

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 70

What is the derivative of

|x - 1|

at

x = 2 ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 71

If

z = f o f (x)

, where

f (x) = x^{2}

, then what is

\frac{d z}{d x}

equal to?

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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 72

What is the derivative of

\sqrt{\frac{1 + \cos x}{1 - \cos x}} ?