differeniate y =log(x²+3)
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Step-by-step explanation:
There are 2 possible approaches.
Approach 1
differentiate using the
chain rule
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
d
d
x
(
log
(
f
(
x
)
)
)
=
1
f
(
x
)
.
f
'
(
x
)
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
y
=
log
(
x
2
)
⇒
d
y
d
x
=
1
x
2
.
d
d
x
(
x
2
)
=
1
x
2
×
2
x
=
2
x
Approach 2
Using the
law of logs
then differentiate.
Reminder
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
log
x
n
=
n
log
x
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−−
y
=
log
x
2
=
2
log
x
⇒
d
y
d
x
=
2
×
1
x
=
2
x
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