Use logarithmic differentiation to find dy/dx

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y
=
(
x
2
−
3
)
y
=
(
x
2
-
3
)
Find the Derivative - d/dx
Differentiate using the Power Rule,
d
d
x
[
x
n
]
=
n
x
n
−
1
d
d
x
[
x
n
]
=
n
x
n
-
1
.
2
x
2
x
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y
=
(
x
2
−
3
)
y
=
(
x
2
-
3
)
Solve for y
Remove parentheses.
y
=
x
2
−
3
y
=
x
2
-
3
y
=
(
x
2
−
3
)
y
=
(
x
2
-
3
)
Graph
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
−
3
)
(
0
,
-
3
)
Focus:
(
0
,
−
11
4
)
(
0
,
-
11
4
)
Axis of Symmetry:
x
=
0
x
=
0
Directrix:
y
=
−
13
4
y
=
-
13
4
x
y
−
2
1
−
1
−
2
0
−
3
1
−
2
2
1
xy-21-1-20-31-221
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image of graph
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y
=
(
x
2
−
3
)
y
=
(
x
2
-
3
)
Find dy/dx
Differentiate each term with respect to
x
x
, then solve for
y
'
y
.
d
y
d
x
=
2
x

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