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Differentiation: Seeds Institute

This document contains 20 questions related to differentiation. The questions cover a range of topics including differentiation of polynomials, trigonometric functions, logarithmic functions, and implicit differentiation. For each question, the correct answer is provided in brackets after the question.

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Ashwin Jambhulkar
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55 views2 pages

Differentiation: Seeds Institute

This document contains 20 questions related to differentiation. The questions cover a range of topics including differentiation of polynomials, trigonometric functions, logarithmic functions, and implicit differentiation. For each question, the correct answer is provided in brackets after the question.

Uploaded by

Ashwin Jambhulkar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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SEEDS INSTITUTE

DIFFERENTIATION

Date 12/05/2011

Class XII

DPP
y' 1 a
b
c
ax
bx
c

1, prove that
.
y x a x b x c x
( x a)( x b)( x c ) ( x b)( x c ) ( x c)
2

1. If

m n

n p

pm

sin m x
sin n x
px
sin
.
, then f '( x ) is equal to? [Ans. f '( x ) 0 ]
2. If f ( x)
.
n
p
m
sin
x
sin
x
sin
x

1
1
1
dy
dy

0]
3. If y
then
is equal to ? [Ans.





1 x x
1 x x
1 x x
dx
dx
1
4. If ( x) log 5 log3 x, then '(e) is equal to ?
[Ans. '(e)
]
e log 5
dy
2 x 1
5. If y f 2 and f '( x ) sin 2 , then
is equal to ?
dx
x 1
2

[Ans.
6. If f ( x) log x (log x), then f '( x ) at x e is ?

7. If y

2
a 2 b2

2
dy
2 x 1 2 2 x 2 x
sin 2
2
2
dx
x 1 ( x 1)
1
[Ans.
]
e

ab
x
tan
, a b 0, then ?
ab
2

tan 1

[Ans.

dy
1

and
dx a b cos x

d2y
b sin x

2
dx
( a b cos x) 2
8. If x y e x y then
9. If y tan 1

dy
is equal to ?
dx

x 1 x2
x 1 x2

10. If y cos 1

, then

1 x2 1

dy
is equal to ?
dx

, then

dy
log x

]
dx (1 log x) 2
dy
1

[Ans.
]
dx
1 x2
[ Ans.

dy
is equal to ?
dx

[Ans.

dy
1

]
dx 2(1 x 2 )

2 1 x2
1
1
1
dy
1
tan 1 2
tan 1 2
.... to n terms, then
11. If y tan 2
is equal to ?
x x 1
x 3x 3
x 5x 7
dx
dy
1
1

[Ans.
]
2
dx 1 ( x n) 1 x 2
dy
dy
2 and x 3 at t 0, then
12. Let y x 3 8 x 7 and x f (t ). If
at t 0 is given by ?
dt
dx
2
[Ans.
]
19
1
3
13. If f ( x) | cos x |, then f ' is equal to ?
[Ans.
]
2
4
14. If

d 1 x 4 x8
ax3 bx then ?

2
4
dx 1 x x

[Ans. a = 4, b = -2]

..............................................................................................................................................................................................................................................................
Ring Road Manendragarh (C.G.) Contact :- 9926750576, 9424953277
..

15. If y e tan x , then cos 2 x


16. If y sin x, then

d2y
is equal to ?
dx 2

d2
(cos 7 x) is equal to ?
2
dy

[Ans. (1 sin 2 x)

dy
]
dx

[Ans. 35cos3 x 42cos5 x ]

17. If f ( x) x 2 6 x 9, then f '( x ) is equal to ? [Ans. 1 for x 3 ]


dy
18. If sin y x cos(a y ), then
is equal to ?
[Ans.
dx
2
1 1 (log x )
, then f '(e) is equal to ?
19. If f ( x) cos
[Ans.
2
1 (log x)
dy
20. If y (1 x1/ 4 )(1 x1/ 2 )(1 x1/ 4 ) , then
is equal to ?
[Ans.
dx

cos 2 (a y )
]
cos a
1
]
e
1]

..............................................................................................................................................................................................................................................................
Ring Road Manendragarh (C.G.) Contact :- 9926750576, 9424953277
..

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