AP Calculus AB Quiz
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DIFFERENTIATION: COMPOSITE, IMPLICIT, AND INVERSE FUNCTIONS
Question 1
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Let
z
(
x
)
=
sin
(
x
2
+
1
)
z(x)=\sqrt{\sin(x^2+1)}
z
(
x
)
=
sin
(
x
2
+
1
)
. What is
z
′
(
x
)
z'(x)
z
′
(
x
)
?
A
cos
(
x
2
+
1
)
2
sin
(
x
2
+
1
)
\dfrac{\cos(x^2+1)}{2\sqrt{\sin(x^2+1)}}
2
sin
(
x
2
+
1
)
cos
(
x
2
+
1
)
B
2
x
cos
(
x
2
+
1
)
2
sin
(
x
2
+
1
)
\dfrac{2x\cos(x^2+1)}{2\sqrt{\sin(x^2+1)}}
2
sin
(
x
2
+
1
)
2
x
cos
(
x
2
+
1
)
C
2
x
sin
(
x
2
+
1
)
2
sin
(
x
2
+
1
)
\dfrac{2x\sin(x^2+1)}{2\sqrt{\sin(x^2+1)}}
2
sin
(
x
2
+
1
)
2
x
sin
(
x
2
+
1
)
D
cos
(
x
2
+
1
)
sin
(
x
2
+
1
)
\dfrac{\cos(x^2+1)}{\sqrt{\sin(x^2+1)}}
sin
(
x
2
+
1
)
cos
(
x
2
+
1
)
E
x
cos
(
x
2
+
1
)
sin
(
x
2
+
1
)
\dfrac{x\cos(x^2+1)}{\sin(x^2+1)}
sin
(
x
2
+
1
)
x
cos
(
x
2
+
1
)
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