AP Calculus BC Quiz
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DIFFERENTIATION: COMPOSITE, IMPLICIT, AND INVERSE FUNCTIONS
Question 1
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In a model,
g
(
x
)
=
arctan
(
5
x
−
1
)
g(x)=\arctan(5x-1)
g
(
x
)
=
arctan
(
5
x
−
1
)
. What is
g
′
(
x
)
g'(x)
g
′
(
x
)
?
A
5
1
−
(
5
x
−
1
)
2
\dfrac{5}{\sqrt{1-(5x-1)^2}}
1
−
(
5
x
−
1
)
2
5
B
5
1
+
(
5
x
−
1
)
2
\dfrac{5}{1+(5x-1)^2}
1
+
(
5
x
−
1
)
2
5
C
5
1
+
(
5
x
−
1
)
2
\dfrac{5}{\sqrt{1+(5x-1)^2}}
1
+
(
5
x
−
1
)
2
5
D
−
5
1
+
(
5
x
−
1
)
2
-\dfrac{5}{1+(5x-1)^2}
−
1
+
(
5
x
−
1
)
2
5
E
5
1
−
(
5
x
−
1
)
2
\dfrac{5}{1-(5x-1)^2}
1
−
(
5
x
−
1
)
2
5
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