Derivative of log tan^-1 x using first principle
Answers
Answered by
2
1
(
tan
−
1
x
)
(
x
2
+
1
)
Explanation:
Given:
y
=
ln
(
tan
−
1
x
)
.
Use the chain rule, which states that,
d
y
d
x
=
d
y
d
u
⋅
d
u
d
x
Let
u
=
tan
−
1
x
,
∴
d
u
d
x
=
1
x
2
+
1
.
Then,
y
=
ln
u
,
∴
d
y
d
u
=
1
u
.
Combining, we get:
d
y
d
x
=
1
u
⋅
1
x
2
+
1
=
1
u
(
x
2
+
1
)
Replacing back
u
=
tan
−
1
x
, we get:
=
1
(
tan
−
1
x
)
(
x
2
+
1
)
Similar questions