Question

differentiate ex/(1+x^2)

Answer 1

given eqn is the main part of answer

Answer 2

The answer is
=
x
e
x
(
1
+
x
)
2
Explanation:
We need the differentiation of a quotient
(
u
v
)
'
=
u
'
v
−
u
v
'
v
2
Here,
u
=
e
x
,
⇒
,
u
'
=
e
x
v
=
1
+
x
,
⇒
,
v
'
=
1
Therefore,
d
y
d
x
=
e
x
(
x
+
1
)
−
e
x
(
1
+
x
)
2
=
x
e
x
+
e
x
−
e
x
(
1
+
x
)
2
=
x
e
x
(
1
+
x
)
2