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IB
Medium
Calculus
10–12
If
f
(
x
)
=
x
x
+
1
f(x) = \frac{x}{x + 1}
f
(
x
)
=
x
+
1
x
, what is
f
′
(
1
)
f'(1)
f
′
(
1
)
?
Se
f
(
x
)
=
x
x
+
1
f(x) = \frac{x}{x + 1}
f
(
x
)
=
x
+
1
x
, quanto vale
f
′
(
1
)
f'(1)
f
′
(
1
)
?
Answer options
A.
\frac{1}{4}
B.
\frac{1}{2}
C.
1
D.
-\frac{1}{4}
Check Answer
Solution
Step 1 of 3
1.
Quotient rule:
f
′
(
x
)
=
(
x
+
1
)
−
x
(
x
+
1
)
2
=
1
(
x
+
1
)
2
f'(x) = \frac{(x + 1) - x}{(x + 1)^{2}} = \frac{1}{(x + 1)^{2}}
f
′
(
x
)
=
(
x
+
1
)
2
(
x
+
1
)
−
x
=
(
x
+
1
)
2
1
Next step
Show full solution