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let f r r be the function f x 1 1 e x the value of
Question:
Let f: R → R be the function
f
(
x
)
=
1
1
+
e
−
x
f(x) = \frac{1}{1+e^{-x}}
f
(
x
)
=
1
+
e
−
x
1
The value of the derivative of ƒ at x where f(x) = 0.4 is ______
(rounded off to two decimal places).
Note: R denotes the set of real numbers.
GATE AR - 2024
GATE AR
Updated On:
Nov 20, 2024
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Correct Answer:
0.24
Solution and Explanation
The correct answer is 0.24
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Let
(
f
(
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( f(x) =
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t
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t
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d
t
,
x
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x \in \mathbb{R}
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Match List-I with List-II:
List-I (Function)
List-II (Derivative w.r.t.
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x
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If
sin
y
=
x
sin
(
a
+
y
)
,
then
d
y
d
x
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\text{ If } \sin y = x \sin(a + y), \text{ then } \frac{dy}{dx} \text{ is:}
If
sin
y
=
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sin
(
a
+
y
)
,
then
d
x
d
y
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Match List-I with List-II:
List-I
List-II
The derivative of
log
e
x
\log_e x
lo
g
e
x
with respect to
1
x
\frac{1}{x}
x
1
at
x
=
5
x = 5
x
=
5
is
(I) -5
If
x
3
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x
2
y
+
x
y
2
−
21
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x^3 + x^2y + xy^2 - 21x = 0
x
3
+
x
2
y
+
x
y
2
−
21
x
=
0
, then
d
y
d
x
\frac{dy}{dx}
d
x
d
y
at
(
1
,
1
)
(1, 1)
(
1
,
1
)
is
(II) -6
If
f
(
x
)
=
x
3
log
e
1
x
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f
(
x
)
=
x
3
lo
g
e
x
1
, then
f
′
(
1
)
+
f
′
′
(
1
)
f'(1) + f''(1)
f
′
(
1
)
+
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′′
(
1
)
is
(III) 5
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x
2
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y
=
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(
x
2
)
and
f
′
(
x
)
=
e
x
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′
(
x
)
=
e
x
, then
d
y
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x
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x
d
y
at
x
=
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=
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If
y
=
log
e
[
e
3
x
(
x
−
4
x
+
3
)
3
/
2
]
y = \log_e \left[ e^{3x} \left( \frac{x - 4}{x + 3} \right)^{3/2} \right]
y
=
lo
g
e
[
e
3
x
(
x
+
3
x
−
4
)
3/2
]
, then find
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y
d
x
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