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Byju's Answer
Standard XII
Mathematics
Continuity of Composite Functions
Let f(x) be a...
Question
Let f(x) be a polynomial. Then, the second order derivative of f(e
x
) is
(a) f'' (e
x
) e
2x
+ f'(e
x
) e
x
(b) f'' (e
x
) e
x
+ f' (e
x
)
(c) f'' (e
x
) e
2x
+ f'' (e
x
) e
x
(d) f'' (e
x
)
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Solution
(a) f''(e
x
)e
2x
+ f'(e
x
)e
x
Since f(x) is a polynomial,
∴
f
'
e
x
=
f
'
e
x
e
x
⇒
f
'
'
e
x
=
f
'
'
e
x
(
e
x
)
2
+
f
'
e
x
e
x
=
f
'
'
e
x
e
2
x
+
f
'
e
x
e
x
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2
Similar questions
Q.
Let f(x) be a polynomial in x. Then the second derivation of f
(
e
x
)
, is:
Q.
Let f(x) be a polynomial. Then, the second order derivative of f(e
x
) is
(a) f'' (e
x
) e
2x
+ f'(e
x
) e
x
(b) f'' (e
x
) e
x
+ f' (e
x
)
(c) f'' (e
x
) e
2x
+ f'' (e
x
) e
x
(d) f'' (e
x
)
Q.
The Derivative of
e
x
Q.
f
(
x
)
=
e
x
1
+
e
x
,
I
1
=
f
(
a
)
∫
f
(
−
a
)
x
g
(
x
(
1
−
x
)
)
d
x
,
I
2
=
f
(
a
)
∫
f
(
−
a
)
g
(
x
(
1
−
x
)
)
d
x
,
t
h
e
n
I
2
I
1
=
Q.
If
f
(
x
)
=
e
x
1
+
e
x
,
I
1
=
∫
f
(
a
)
x
g
{
x
(
1
−
x
)
}
f
(
−
a
)
d
x
and
I
2
=
∫
f
(
a
)
g
{
x
(
1
−
x
)
}
f
(
−
a
)
d
x
then
I
2
I
1
equals
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