Using proper substitution differentiate the function w.r.t x cot ¹(√1 + x² + x) Fast its urgent!!!
Answers
Answered by
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Step-by-step explanation:
We have,
y=cot
−1
[
x
1+x
2
+1
]
On differentiating w.r.t x, we get
dx
dy
=
1+(
x
1+x
2
+1
)
2
−1
×
x
2
x(
2
1+x
2
1
×2x+0)−(
1+x
2
+1)
dx
dy
=
x
2
+(
1+x
2
+1)
2
−x
2
×
x
2
(
1+x
2
x
2
)−(
1+x
2
+1)
dx
dy
=
x
2
+(
1+x
2
+1)
2
−1
×[(
1+x
2
x
2
)−(
1+x
2
+1)]
dx
dy
=
x
2
+(
1+x
2
+1)
2
−1
×(
1+x
2
x
2
−1−x
2
−
1+x
2
)
dx
dy
=
x
2
+1+x
2
+1+2
1+x
2
−1
×(
1+x
2
−1−
1+x
2
)
dx
dy
=
2(x
2
+1+
1+x
2
)
1
×(
1+x
2
1+
1+x
2
)
dx
dy
=
2
1+x
2
(1+
1+x
2
)
1
×(
1+x
2
1+
1+x
2
)
dx
dy
=
2×(1+x
2
)
1
Hence, this is the answer.
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