Implicit Differentiation
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Differentiate
x
2
−
y
2
=
4
x^2 - y^2 = 4
x
2
−
y
2
=
4
using implicit differentiation.
QUESTION
What does
d
y
d
x
\frac{dy}{dx}
d
x
d
y
represent in implicit differentiation?
QUESTION
Differentiate
x
y
=
1
\frac{x}{y} = 1
y
x
=
1
with respect to
x
x
x
.
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ANSWER
y
−
x
d
y
d
x
y
2
=
0
\frac{y - x\frac{dy}{dx}}{y^2} = 0
y
2
y
−
x
d
x
d
y
=
0
. Apply quotient rule:
d
d
x
[
x
y
]
=
y
−
x
d
y
d
x
y
2
\frac{d}{dx}[\frac{x}{y}] = \frac{y - x\frac{dy}{dx}}{y^2}
d
x
d
[
y
x
]
=
y
2
y
−
x
d
x
d
y
.
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