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E M B I B E
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
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EASY
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Find
d
y
d
x
, if
y
=
x
sin
x
(a)
1
y
d
y
d
x
=
1
x
+
cot
x
(b)
cot
x
=
d
y
d
x
y
(c)
1
y
d
y
d
x
=
1
x
-
cot
x
(d)
d
y
d
x
=
1
x
+
cot
x
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Important Questions on Differential Coefficient
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
y
=
sin
2
x
1
+
cot
x
+
cos
2
x
1
+
tan
x
,
then
y
′
(
x
)
is equal to
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
g
x
is the inverse function of
f
x
and
f
'
x
=
1
1
+
x
4
,
then
g
'
x
is
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
f
x
=
x
6
+
6
x
,
then
f
′
(
x
)
is equal to
HARD
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
p
x
be a polynomial such that
p
x
-
p
'
x
=
x
n
where
n
is a positive integer. Then,
p
0
equals
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
y
=
sec
tan
-
1
x
, then
d
y
d
x
at
x
=
1
is equal to
HARD
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
f
be a polynomial function such that
f
3
x
=
f
′
x
.
f
′
′
x
,
for all
x
∈
R
.
Then :
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
f
and
g
be differentiable functions such that
f
(
3
)
=
5
,
g
(
3
)
=
7
,
f
′
(
3
)
=
13
,
g
′
(
3
)
=
6
,
f
′
(
7
)
=
2
and
g
′
(
7
)
=
0
.
If
h
(
x
)
=
(
f
o
g
)
(
x
)
,
then
h
′
(
3
)
=
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
y
α
=
2
t
a
n
α
+
c
o
t
α
1
+
t
a
n
2
α
+
1
s
i
n
2
α
,
α
∈
3
π
4
,
π
, then
d
y
d
α
at
α
=
5
π
6
is
EASY
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
sin
y
=
x
sin
a
+
y
, then
d
y
d
x
is
EASY
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If the function
f
x
defined by
f
x
=
x
100
100
+
x
99
99
+
.
.
.
.
.
.
+
x
2
2
+
x
+
1
,
then
f
′
(
0
)
=
EASY
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
f
1
=
1
,
f
'
1
=
3
, then the derivative of
f
f
f
x
+
f
x
2
at
x
=
1
is:
EASY
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
For
x
>
1
, if
2
x
2
y
=
4
e
2
x
-
2
y
, then
1
+
log
e
2
x
2
d
y
d
x
is equal to
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
∫
e
sec
x
sec
x
tan
x
f
x
+
sec
x
tan
x
+
sec
2
x
d
x
=
e
sec
x
f
x
+
C
,
then a possible choice of
f
x
is:
EASY
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
f
:
f
-
x
→
f
x
be a differentiable function. If
f
is even, then
f
′
(
0
)
is equal to
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
f
x
=
log
e
s
i
n
x
,
0
<
x
<
π
and
g
x
=
sin
-
1
(
e
-
x
)
,
(
x
≥
0
)
.
If
α
is a positive real number such that
a
=
f
o
g
'
(
α
)
and
b
=
f
o
g
(
α
)
,
then
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
y
=
y
x
be a function of
x
satisfying
y
1
-
x
2
=
k
-
x
1
-
y
2
, where
k
is a constant and
y
1
2
=
-
1
4
. Then
d
y
d
x
at
x
=
1
2
, is equal to
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
x
k
+
y
k
=
a
k
,
a
,
k
>
0
and
d
y
d
x
+
y
x
1
3
=
0
,
then
k
is
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If for
x
∈
0
,
1
4
,
the derivative of
tan
-
1
6
x
x
1
-
9
x
3
is
x
⋅
g
x
, then
g
x
equals:
HARD
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
Let
f
be a differentiable function such that
f
1
=
2
and
f
'
x
=
f
x
for all
x
∈
R
. If
h
x
=
f
f
x
, then
h
'
1
is equal to :
MEDIUM
Mathematics
>
Differential Calculus
>
Differential Coefficient
>
Basics of Differentiation
If
y
=
x
+
c
1
+
x
2
where
c
is a constant, when
y
is stationary,
x
y
is equal to -