AP Calculus AB Quiz
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DIFFERENTIATION: DEFINITION AND FUNDAMENTAL PROPERTIES
Question 1
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A function is
w
(
x
)
=
ln
(
sin
(
x
2
+
1
)
)
w(x)=\ln\!\left(\sin\!\left(x^2+1\right)\right)
w
(
x
)
=
ln
(
sin
(
x
2
+
1
)
)
. What is
w
′
(
x
)
w'(x)
w
′
(
x
)
?
A
1
sin
(
x
2
+
1
)
\dfrac{1}{\sin(x^2+1)}
sin
(
x
2
+
1
)
1
B
cos
(
x
2
+
1
)
sin
(
x
2
+
1
)
\dfrac{\cos(x^2+1)}{\sin(x^2+1)}
sin
(
x
2
+
1
)
cos
(
x
2
+
1
)
C
2
x
cos
(
x
2
+
1
)
sin
(
x
2
+
1
)
\dfrac{2x\cos(x^2+1)}{\sin(x^2+1)}
sin
(
x
2
+
1
)
2
x
cos
(
x
2
+
1
)
D
2
x
cos
(
x
2
+
1
)
2x\cos(x^2+1)
2
x
cos
(
x
2
+
1
)
E
ln
(
sin
(
x
2
+
1
)
)
⋅
2
x
cos
(
x
2
+
1
)
\ln(\sin(x^2+1))\cdot 2x\cos(x^2+1)
ln
(
sin
(
x
2
+
1
))
⋅
2
x
cos
(
x
2
+
1
)
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