Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 36

MEDIUM

NDA & NA EE

IMPORTANT

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What is the derivative of $\log_{x} 5$ with respect to $\log_{5} x ?$

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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 37

If

e^{y} + x y = e

, then what is the value of

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

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 38

If

3^{x} + 3^{y} = 3^{x + y}

, 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 39

If

f (x) = \cos x, g (x) = \log x

and

y = (g o f) (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 40

If

y = f (x), p = \frac{d y}{d x}

and

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

, then what is

\frac{d^{2} x}{d y^{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 41

If

x = \sin t - t \cos t

and

y = t \sin t + \cos t

, then what is

\frac{d y}{d x}

at point

t = \frac{π}{2} ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 42

If the curve

\sqrt{x} + \sqrt{y} = 1

, then what is the value of

\frac{d y}{d x}

at

(\frac{1}{4}, \frac{1}{4}) ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 24 - Differentiation>Practice Exercise>Q 43

If

y = \frac{1}{\log_{10} x}

, 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 44

If

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

, then what is

\frac{d y}{d x}

equal to?