EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 8th April 2019 Shift 2>Q 16

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JEE Main

IMPORTANT

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If $f (1) = 1, f^{'} (1) = 3$ , then the derivative of $f (f (f (x))) + {(f (x))}^{2}$ at $x = 1$ is:

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Important Questions on Differential Coefficient

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 10th April 2019 Shift 2>Q 17

Let

f (x) = \log_{e} (s i n x), (0 < x < π)

and

g (x) = \sin^{- 1} (e^{- x}), (x \geq 0) .

If

α

is a positive real number such that

a = {(f o g)}^{'} (α)

and

b = (f o g) (α),

then

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 12th April 2019 Shift 1>Q 18

If

e^{y} + x y = e,

the ordered pair

(\frac{d y}{d x}, \frac{d^{2} y}{d x^{2}})

at

x = 0

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 12th April 2019 Shift 2>Q 19

The derivative of

{t a n}^{- 1} (\frac{s i n x - c o s x}{s i n x + c o s x})

with respect to

\frac{x}{2},

where

x \in (0, \frac{π}{2})

, is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 12th January 2019 Shift 1>Q 20

For

x > 1

, if

{(2 x)}^{2 y} = 4 e^{2 x - 2 y}

, then

{(1 + \log_{e} 2 x)}^{2} \frac{d y}{d x}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 12th January 2019 Shift 2>Q 21

Let

f

be a differentiable function such that

f (1) = 2

and

f^{'} (x) = f (x)

for all

x \in R

. If

h (x) = f (f (x))

, then

h^{'} (1)

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 15th April 2018>Q 22

If

x^{2} + y^{2} + \sin y = 4

, then the value of

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

at the point

(- 2, 0)

is :

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 16th April 2018>Q 23

If

x = \sqrt{2^{{cosec}^{- 1} t}}

and

y = \sqrt{2^{\sec^{- 1} t}}, (|t| \geq 1),

then

\frac{d y}{d x}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>JEE Main - 2nd April 2017>Q 24

If for

x \in (0, \frac{1}{4}),

the derivative of

\tan^{- 1} (\frac{6 x \sqrt{x}}{1 - 9 x^{3}})

is

\sqrt{x} \cdot g (x)

, then

g (x)

equals: