Assertion: For x < 0 , d 2 d x 2 log | x | = 1 | x | 2 Reason: For x < 0 , | x | = - x

Assertion is false but Reason is true.

Assertion is true but Reason is false.

Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

Assertion: For x < 0 , d 2 d x 2 log | x | = 1 | x | 2 Reason: For x < 0 , | x | = - x

Assertion is false but Reason is true.

For any quadratic polynomial f ( x ) , it is true that f x = f a + f ' a ( x - a ) + f " a 2 ! x - a 2 where a is any real number. If 3 x 2 + 4 x + 7 ( x - 2 ) 3 = A ( x - 2 ) 3 + B ( x - 2 ) 2 + C ( x - 2 ) and g ( x ) = 3 x 2 + 4 x + 7 then A + B + C =

g ( 2 ) + g ' ( 2 ) + g " ( 2 )

If y = cos - 1 ( tan h x ) + sin h ( sin 6 x ) , then d y d x =

- 1 cos h x + 6 cos 6 x cos h sin 6 x

1 cos h x - 6 cos 6 x cos h sin 6 x

- 1 cos h x - 6 cos 6 x cos h sin 6 x

1 cos h x + 6 cos 6 x cos h sin 6 x

If x = 5 ( 1 - sin t ) , y = 5 ( t + cos t ) , then d x d y =

cos t / 2 - sin t / 2 cos t / 2 + sin t / 2

If y = cos - 1 ( tan h x ) + sin h ( sin 6 x ) , then d y d x =

- 1 cos h x + 6 cos 6 x cos h sin 6 x

1 cos h x - 6 cos 6 x cos h sin 6 x

- 1 cos h x - 6 cos 6 x cos h sin 6 x

1 cos h x + 6 cos 6 x cos h sin 6 x

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Differentiation>TS EAMCET 2020 (9-Sep Shift-1)>Q 1

MEDIUM

TS EAMCET

IMPORTANT

Earn 100

Assertion: For $x < 0, \frac{d^{2}}{d x^{2}} (\log | x |) = \frac{1}{| x |^{2}}$
Reason: For $x < 0, | x | = - x$

18.18% studentsanswered this correctly

Important Questions on Differentiation

HARD

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Differentiation>TS EAMCET 2019 (03-May Shift-2)>Q 2

Suppose,

f (x) = e^{- \sqrt{x}} + e^{- \frac{1}{x^{2}}}

. If

f^{''} (x) = α \cdot \frac{e^{- \sqrt{x}}}{x} (1 + \frac{1}{\sqrt{x}}) + β \cdot \frac{e^{- \frac{1}{x^{2}}}}{x^{4}} (3 - \frac{2}{x^{2}})

, then

(α, β) =

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Differentiation>TS EAMCET 2019 (03-May Shift-2)>Q 3

The derivative of

\cos h^{- 1} x

with respect to

\log x

at

x = 5

is

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Differentiation>TS EAMCET 2021 (04-Aug Shift-1)>Q 4

For any quadratic polynomial

f (x),

it is true that

f (x) = f (a) + f' (a) (x - a) + \frac{f " (a)}{2!} {(x - a)}^{2}

where

a

is any real number.
If

\frac{3 x^{2} + 4 x + 7}{(x - 2)^{3}} = \frac{A}{(x - 2)^{3}} + \frac{B}{(x - 2)^{2}} + \frac{C}{(x - 2)}

and

g (x) = 3 x^{2} + 4 x + 7

then

A + B + C =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Differentiation>TS EAMCET - 5 August 2021 Shift 2>Q 5

If

y = \cos^{- 1} (\tan h x) + \sin h (\sin 6 x),

then

\frac{d y}{d x} =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Differentiation>TS EAMCET 2020 (9-Sep Shift-1)>Q 6

For

x \neq - 1, y \neq - 1

, if

x = \frac{1 - \sqrt[3]{y}}{1 + \sqrt[3]{y}}

, then

\frac{d x}{d y} =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Differentiation>TS EAMCET 2018 (04-May Shift-1)>Q 7

Match the items given in List- $I$ with those of the items of List- $II$

	List - $I$		List - $II$
$(a)$	If $y = \|x\| + \|x - 2\|$ then at $x = 2, \frac{d y}{d x} =$	$(i)$	$1$
$(b)$	If $f (x) = \|\cos 2 x\|$ , then $f^{'} (\frac{π}{4} +) =$	$(ii)$	$0$
$(c)$	If $f (x) = \sin π [x]$ where $[\cdot]$ denotes the greatest integer function, then $f^{'} (1 -) =$	$(iii)$	$- 2$
$(d)$	If $f (x) = \log \|x - 1\|, x \neq 1$ then $f^{'} (\frac{1}{2}) =$	$(iv)$	does not exits
		$(v)$	$\frac{1}{2}$