Question

Use logarithmic differentiation to find dy/dx

Answer 1

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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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You are currently in the Algebra section, but it looks like you might be trying to do calculus. You might find more of the topics and symbols you need if you switch your subject over to Calculus.
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
x y -2 1 -1 -2 0 -3 1 -2 2 1
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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