Find dy/dx if y = 7^x log 7
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Answer:
Differentiate using the Quotient Rule which states that
d
d
x
[
f
(
x
)
g
(
x
)
]
is
g
(
x
)
d
d
x
[
f
(
x
)
]
−
f
(
x
)
d
d
x
[
g
(
x
)
]
g
(
x
)
2
where
f
(
x
)
=
7
x
and
g
(
x
)
=
log
7
(
x
)
.
log
7
(
x
)
d
d
x
[
7
x
]
−
7
x
d
d
x
[
log
7
(
x
)
]
log
7
2
(
x
)
Differentiate using the Exponential Rule which states that
d
d
x
[
a
x
]
is
a
x
ln
(
a
)
where
a
=
7
.
log
7
(
x
)
(
7
x
ln
(
7
)
)
−
7
x
d
d
x
[
log
7
(
x
)
]
log
7
2
(
x
)
The derivative of
log
7
(
x
)
with respect to
x
is
1
x
ln
(
7
)
.
log
7
(
x
)
⋅
7
x
ln
(
7
)
−
7
x
1
x
ln
(
7
)
log
7
2
(
x
)
Combine
1
x
ln
(
7
)
and
7
x
.
log
7
(
x
)
⋅
7
x
ln
(
7
)
−
7
x
x
ln
(
7
)
log
7
2
(
x
)
Simplify.
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7
x
ln
(
7
)
log
7
(
x
)
−
7
x
x
ln
(
7
)
log
7
2
(
x
)
Step-by-step explanation:
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