Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 21

EASY

NDA & NA EE

IMPORTANT

Earn 100

What is the differentiation of $\log_{x} x$ with respect to $\log x ?$

50% studentsanswered this correctly

Important Questions on Differentiation

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 23

If

x = t + \frac{1}{t}, y = t - \frac{1}{t}

then

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

is equal to

MEDIUM

NDA & NA EE

IMPORTANT

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

If

y = \sin x + e^{x}

, then

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

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 26

If

y = (1 + x^{\frac{1}{4}}) (1 + x^{\frac{1}{2}}) (1 - x^{^{\frac{1}{4}}})

, then what is

\frac{d y}{d x}

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 28

If

x = k (θ + \sin θ)

and

y = k (1 + \cos θ)

, then what is the derivative of

y

with respect to

x

at

θ = \frac{π}{2} ?

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 30

If for a continuous function

f

,

f (0) = f (1) = 0

,

f^{'} (1) = 2

and

g (x) = f (e^{x}) e^{f (x)}

, then

g^{'} (0)

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 31

If

x = \cos (2 t)

and

y = \sin^{2} t

, then what is

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

equal to?

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 32

If

y = e^{2 x}

, then

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

is equal to

HARD

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 34

If

y = \tan^{- 1} (\frac{\log_{e} (\frac{e}{x^{2}})}{\log_{e} (e x^{2})}) + \tan^{- 1} (\frac{3 + 2 \log_{e} x}{1 - 6 \log_{e} x})

, then

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

is equal to