AP Calculus AB Quiz
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DIFFERENTIATION: COMPOSITE, IMPLICIT, AND INVERSE FUNCTIONS
Question 1
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For the relation
x
ln
y
+
y
ln
x
=
10
x\ln y+y\ln x=10
x
ln
y
+
y
ln
x
=
10
, what is
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
at
(
x
,
y
)
(x,y)
(
x
,
y
)
?
A
d
y
d
x
=
−
ln
y
+
y
x
x
y
+
ln
x
\dfrac{dy}{dx}=-\dfrac{\ln y+\frac{y}{x}}{\frac{x}{y}+\ln x}
d
x
d
y
=
−
y
x
+
ln
x
ln
y
+
x
y
B
d
y
d
x
=
−
ln
y
+
x
y
x
y
+
ln
x
\dfrac{dy}{dx}=-\dfrac{\ln y+\frac{x}{y}}{\frac{x}{y}+\ln x}
d
x
d
y
=
−
y
x
+
ln
x
ln
y
+
y
x
C
d
y
d
x
=
−
ln
y
+
y
x
ln
x
\dfrac{dy}{dx}=-\dfrac{\ln y+\frac{y}{x}}{\ln x}
d
x
d
y
=
−
ln
x
ln
y
+
x
y
D
d
y
d
x
=
−
ln
y
ln
x
\dfrac{dy}{dx}=-\dfrac{\ln y}{\ln x}
d
x
d
y
=
−
ln
x
ln
y
E
d
y
d
x
=
ln
y
+
y
x
x
y
+
ln
x
\dfrac{dy}{dx}=\dfrac{\ln y+\frac{y}{x}}{\frac{x}{y}+\ln x}
d
x
d
y
=
y
x
+
ln
x
ln
y
+
x
y
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