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ruslelena [56]
2 years ago
15

Differentiate cosecx^2​

Mathematics
1 answer:
alexgriva [62]2 years ago
6 0

Answer:csc

2

(

x

)

=

1

sin

2

(

x

)

Step-by-step explanation:

d

d

x

[

csc

2

(

x

)

]

=

−

2

cot

x

csc

2

x

Explanation:

csc

2

(

x

)

=

1

sin

2

(

x

)

d

d

x

[

csc

2

(

x

)

]

=

d

d

x

[

1

sin

2

(

x

)

]

d

d

x

[

1

sin

2

(

x

)

]

=

d

d

x

[

[

sin

(

x

)

]

−

2

]

let

u

=

sin

x

d

d

x

[

[

sin

(

x

)

]

−

2

]

=

d

d

u

[

u

−

2

]

d

d

x

[

sin

x

]

d

d

u

[

u

−

2

]

=

−

2

u

−

3

d

d

x

[

sin

x

]

=

cos

x

d

d

x

[

[

sin

(

x

)

]

−

2

]

=

−

2

u

−

3

cos

x

=

−

2

cos

x

sin

3

x

cos

x

sin

x

=

cot

x

⇒

−

2

cos

x

sin

3

x

=

−

2

cot

x

sin

2

x

1

sin

2

x

=

csc

2

x

⇒

−

2

cot

x

csc

2

x

d

d

x

[

csc

2

(

x

)

]

=

−

2

cot

x

csc

2

x

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