differentiation assignment.pdf for class 11th

Physics

1. Find
dy
dx
of the given functions
1.y = x
n + 2
, where n is constant
2.y = x
3
3.y = x
–n
, where n is constant
4.y = x
–4
5.
1
n
y = x , where n is constant and n0z
6.
1
2
y = x
7.
2
3
y = x
"
8.
y = ax
3
, where a is a constant
9.
1
4
1
y = x
2
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Differentiate with respect to x
a x
2
b x
4
c x d x
9
e x
−3
f x
−1

g 4x
2
h 7x i 2x
5
j 3 k 8x
−2
l11x
−4
11 (x
7/2
)
dx
d
is equal to
(1)x
−5/2
2
7
(2)x
5/2
2
7
−
2
(3)
7
x
5/2
(4)x
5/2
7
2
12 ⎟
⎠
⎜
⎝x
3
1
dx
d⎛⎞
is equal to
(1)
x
4
−3
(2)
3
x
2
(3)
3
x
2
− (4) 3x
2
1
dx
d
(x
3/2
) is :
(1)
2
3
x
1/2
(2)
2
3
x
5/2
(3)
2
3
x
7/2
(4)
2
3
x
9/2
14 ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
x
1
dx
d
(1)
x2
1
(2) x (3)–
2x
3/2
1
(4)
2x
3/2
1
15The value of
dy
for y = 5x will be -
dx
(A) 5 (B)
2
5x
2
(C) zero (D) 10x
2
16
dx
d
(πx
2
) is equal to
(1) 2πx (2)πx (3) 2x (4)
2
πx
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2. 1. If y = x
3
+ 2x
2
+ 7x + 8 then
dx
dy
will be -
(A) 3x
2
+ 2x + 15 (B) 3x
2
+ 4x+7 (C) x
3
+ 2x
2
+ 15(D)x
3
+ 4x + 7
2.
If y = x
2
sin x , then
dx
dy
will be -
(A) x
2
cos x + 2x sin x
(B) 2x sin x (C) x
2
cos x
(D) 2 x cos x
3. If y = e
x
. cot x then
dx
dy
will be
(A) e
x
cot x – cosec
2
x (B) e
x
cosec
2
x (C) e
x
[cot x – cosec
2
x]
(D) e
x
cot x
dx
dy
will be4. If y = x nx then
(A) nx + x (B) 1 + n x (C)nx (D) 1
dx
dy
5. y = 4 + 5x + 7x
3
. Find
(A) 5 - 21x
2
(B) 5 + 21x
2
(C) 9 + 7x
2
(D) 5 + 21x
x
3
1
x
1
Find
dx
dy
6. y = x +x
2
. +
(A)1 + 2x –
x
42
3
x
1
(B) 1 + 2x –
4
2
x
(C) 1 – 2x –
4
3
x
(D) 1 + 2x –
3
3
x
7. If f(x) =
x2
x2
The value f (–1) is
(A)
3
1
(B)
3
1
(C)3 (D) –3
8. y = x
2
+
x
1
2
.Find
dx
dy
(A) 2x –
x
3
2
(B)2x –
4
2
x
(C)2x +
x
3
2
(D) None of these
2
x
1
2
x
1
2
x
1
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3. )x(tan
dx
d
is equal to
(1) sec
2
x (2)cotx
(3)– sec
2
x (4)– cot x
1
dx
d
(x
3
+ 4x
2
+ 1) is equal to
(1) cxx
3
4
4
x
3
4
+++ (2)3x
2
+ 8x
(3)
4
x
4
+ 8x (4) 3x
2
+
4
x
4
x
3
11 ⎟
⎠
⎞
⎜
⎝
⎛
+++ xtanxlog
x
1
x
dx
d

(1) 1 –
2
x
1
+ sec
2
x
(2) 1 +
x
1
+ sec
2
x
(3) 1 +
2
x
1
+
x
1
+ sec
2
x
(4) 1 –
2
x
1
+
x
1
+ sec
2
x
1
2
x
1
x
dx
d
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+ is equal to
(1)
2
x
1
1+ (2)
2
x
1
1+−
(3)
2
x
1
1− (4) x
2
– 1
1
d
(x
4
– 2 sin x + 3 cos x)
dx
(A)4x
3
– 2 cos x + 3 sin x
(B) 3x
2
+ 2 cosx + 3 sin x
(C) 4x
3
+ 2 cosx – 3 sin x
(D) 4x
3
– 2 cos x – 3 sin x
dy
at x = 1 is -
dx
If14. y = x
3
+ 2x + 1 then
(A) 6 (B) 7
(C) 8 (D) 5
dy
is -
dx
y15. = secx + tanx , value of
(A)sec
2
x + tan x (B)tan
2
x + sec x
(C)secx (tanx + secx) (D) sec x (1 + sec x)
dx
d
x1
(x
2
+1)
+
(A)
2
2
(x+1)
x+2x−1
(B)
2
(x+1)
x
2
−2x+1

(C)
x+1
x
2
+2x−1
(D)
2
2
(x+1)
x+2x+1

dx
d
⎟
⎠
⎜
⎝
⎛
+1+
x
32
1
x
1 ⎞

(A)x +
x
1
2
+
x
3
1
(B)
x
4
3
(C)x –
x
1
2
–
x
3
3
(D)
–2
–
x
3
–2
–
x x
2
3
16
17.
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4. Q.1
dx
d
x2sin
(A) (sin 2x)
–1/2
(B) cos 2x (sin 2x)
–1/2
(C) 2 cos 2x (sin 2x)
–1/2
(D) cos 2x (sin 2x)
1/2
Q.2
dx
d
xtan
(A) 2 sec
2
x (tan x)
–1/2
(B)
2
1
sec
2
x (tan x)
–1
(C)
2
1
(tan x)
–1/2
(D) 2 (tan x)
–1/2
Q.3
dx
d
sin (log x)
(A) cos (log x) (B) log (cos x) (C) x cos (log x) (D)
x
)xcos(log
Q.4
dx
d
1x 2
2
+
(A) 2x (2x
2
+ 1)
1/2
(B) 2x (2x
2
+ 1)
–1/2
(C) (2x
2
+ 1)
1/2
(D) (2x
2
+ 1)
–1/2
Q.5
dx
d
x2
e
(A)
x2
e
x2
(B) x2
x2
e (C)
x2
e (D)
2/ 1
)x2(
e
−
Q.6
dx
d
sin
2
(x
2
)
(A)2x sin
2
x
2
cos x
2
(B)4x sin x
2
cos x (C)2x sin 2x
2
(D)4x sin x cos x
2
Q.7 y = cos
2
x is given, then
dx
dy
is -
(A)–2 sinx cos x(B)2 sin x cos x (C)sin
2
x (D)none of these
Q.8 If y = log (tanx), then
dx
dy
is -
(A)
xtan
xcos
2
(B)
xtan
1
(C)
xtan
xsec
2
(D)log(sec
2
x)
Q.9 If y = sin(2x
2
), then
dx
dy
is -
(A)4x cos (2x
2
) (B)2 cos (2x
2
)(C) 4 cos (2x
2
) (D)– 4 cos (2x
2
)
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5. Q.10 If y = sin
2
x – 2 tan
2
x , then
dx
dy
at x =
4
π
is -
(A)– 11 (B)– 7 (C)– 13 (D)– 15
Q.11 If y = x
3
+ 2x + 1 then
dx
dy
at x = 1 is -
(A) 6 (B) 7 (C) 8 (D) 5)
Q.12
dx
d
[log(cosx)] is :
(1)–tan x (2) tan x (3) cot x (4)–cot x
Q.13
dy
d
(y + 2)
2
is equal to
(1) 2y + 4 (2) 2y – 4 (3) 4 + y
2
(4)2(y + 1)
14.Slope of graph y = tanx drawn between y and x, at x = is :
4
(A) 0 (B) 1 (C) 2 (D)
2
1
15.Equation of straight line is 2x + 3y = 5. Slope of the straight line is :
(B) 2/3 (C) –2/3 (D) –3/2(A) 3/2
dt
dy
16.y = 5sin (3 t + )
where and are constant
Find
(A) 15

co

s (3

t

+ )
(C) 15 cos (3 t + )
(B) 15

cos

(3 t)
(D) 5 cos (3 t + )
dt
17.If y = e
kt
then
dy
will be
(A) e
kt
(B) e
kt
/ k (C) te
kt
(D) ke
kt
ss
18.Differentiation of sin(x
2
) w.r.t. x is -
(A) cos (x
2
) (B) 2x cos(x
2
) (C) x
2
cos(x
2
) (D) – cos (2x)
19.Double differentiation of displacement w.r.t. time is :
(A) acceleration (B) velocity (C) force (D) none
2
dx
2
If y = x
3
then
dy
is -
20.
(A) 6x
2
(B) 6x (C) 3x
2
(D) 3x
dx
2
d
2
y
will be :21.If y = sinx, then
(A) cos x (B) sin x (C) – sin x (D) sin x + C
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6. BM solutions 1,2,3