Implicit Differentiation
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Differentiate
x
3
+
y
3
=
6
x
y
x^3 + y^3 = 6xy
x
3
+
y
3
=
6
x
y
implicitly.
QUESTION
Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
x
2
+
2
y
2
=
3
x
y
x^2 + 2y^2 = 3xy
x
2
+
2
y
2
=
3
x
y
.
QUESTION
Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
x
y
=
1
\frac{x}{y} = 1
y
x
=
1
.
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ANSWER
d
y
d
x
=
y
x
\frac{dy}{dx} = \frac{y}{x}
d
x
d
y
=
x
y
. From
x
y
=
1
\frac{x}{y} = 1
y
x
=
1
, we get
x
=
y
x = y
x
=
y
, so slopes are equal.
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