y=log(x+√x²-a²). find dy\dx if
Answers
Answer:
Step-by-step explanation:
y
d
x
=
2
x
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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See all questions in Differentiating Logarithmic Functions without Base e
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y
d
x
=
2
x
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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f
(
x
)
=
log
b
(
g
(
x
)
)
?
What is the derivative of
f
(
x
)
=
log
(
x
2
+
x
)
?
What is the derivative of
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(
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)
=
log
4
(
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x
+
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)
?
What is the derivative of
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(
x
)
=
x
⋅
log
5
(
x
)
?
What is the derivative of
f
(
x
)
=
e
4
x
⋅
log
(
1
−
x
)
?
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f
(
x
)
=
log
(
x
)
x
?
What is the derivative of
f
(
x
)
=
log
2
(
cos
(
x
)
)
?
What is the derivative of
f
(
x
)
=
log
11
(
tan
(
x
)
)
?
What is the derivative of
f
(
x
)
=
√
1
+
log
3
(
x
)
?
What is the derivative of
f
(
x
)
=
(
log
6
(
x
)
)
2
?
See all questions in Differentiating Logarithmic Functions without Base e
Impact of this question
14689 views around the world
You can reuse this answer
Creative Commons License
iOS
Answer:
Step-by-step explanation:
Given:
We need to derivate y and find dy/dx.
We gonna use Chain rule to find it.
Therefore,