AP Calculus BC Quiz
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DIFFERENTIATION: COMPOSITE, IMPLICIT, AND INVERSE FUNCTIONS
Question 1
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The relation
x
3
+
y
3
=
6
x
y
x^3+y^3=6xy
x
3
+
y
3
=
6
x
y
defines
y
y
y
implicitly. What is
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
?
A
6
y
−
3
x
2
3
y
2
−
6
x
\dfrac{6y-3x^2}{3y^2-6x}
3
y
2
−
6
x
6
y
−
3
x
2
B
6
y
−
3
x
2
3
y
2
\dfrac{6y-3x^2}{3y^2}
3
y
2
6
y
−
3
x
2
C
6
−
3
x
2
3
y
2
−
6
x
\dfrac{6-3x^2}{3y^2-6x}
3
y
2
−
6
x
6
−
3
x
2
D
6
y
−
3
x
2
−
6
x
\dfrac{6y-3x^2}{-6x}
−
6
x
6
y
−
3
x
2
E
3
x
2
−
6
y
3
y
2
−
6
x
\dfrac{3x^2-6y}{3y^2-6x}
3
y
2
−
6
x
3
x
2
−
6
y
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