Implicitly Defined Functions
AP Precalculus · Flashcards · Application
AP PRECALCULUS · FLASHCARDS
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QUESTION
Differentiate
x
2
−
2
x
y
+
y
2
=
0
x^2 - 2xy + y^2 = 0
x
2
−
2
x
y
+
y
2
=
0
implicitly.
QUESTION
Differentiate implicitly
x
3
+
y
3
=
3
x
y
x^3 + y^3 = 3xy
x
3
+
y
3
=
3
x
y
.
QUESTION
Differentiate
x
2
y
+
y
3
=
7
x^2y + y^3 = 7
x
2
y
+
y
3
=
7
implicitly.
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ANSWER
2
x
y
+
x
2
d
y
d
x
+
3
y
2
d
y
d
x
=
0
2xy + x^2 \frac{dy}{dx} + 3y^2 \frac{dy}{dx} = 0
2
x
y
+
x
2
d
x
d
y
+
3
y
2
d
x
d
y
=
0
. Apply the product rule and chain rule to each term.
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