dy
If y = cot
1-37
3r-
dy
3
1+
1-2
1
(C)
1
1+
3(1+*?)
Answers
Answered by
1
Answer:
Step-by-step explanation:
We have,
y=cot
−1
(
3x−x
3
1−3x
2
);∣x∣>
3
1
Put x=cotθ⇒θ=cot
−1
x
Then,
Put and we get,
y=cot
−1
(
3cotθ−cot
3
θ
1−3cot
2
θ
)
y=tan
−1
(
1−3cot
2
θ
3cotθ−cot
3
θ
)
=tan
−1
(
3cot
2
θ−1
cot
3
θ−3cotθ
)
=tan
−1
cot3θ
=tan
−1
tan(
2
π
−3θ)
=
2
π
−3θ
y=
2
π
−3cot
−1
x
On differentiating and we get,
dx
dy
=
dx
d
(
2
π
−3cot
−1
x)
=(0−3(−
1+x
2
1
))
=
1+x
2
3
Hence, this is the answer.
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