Math, asked by architkash2004, 1 month ago

Using proper substitution differentiate the function w.r.t x cot ¹(√1 + x² + x) Fast its urgent!!!​

Answers

Answered by BANGTANARMYlucky
6

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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