Question

y=(sin inverse x)^2 then prove
​

Answer 1

Answer:

y=(sin

−1

x)

2

on differentiating wrt x we get

⇒

dx

dy

=2sin

−1

x×

1−x

2

1

_______ (1)

again differentiating wrt x we get

⇒

dx

2

d

2

y

=2

(1−x

2

)

1−x

2

1

×

1−x

2

−sin

−1

×

2

1−x

2

1x−2x

(1−x

2

)

dx

2

d

2

y

=2[1+x

1−x

2

sin

−1

x

]

(1−x

2

)

dx

2

d

2

y

−2x

1−x

2

sin

−1

x

=2

From equation (1)

(1−x

2

)

dx

2

dy

2

−x

dx

dy

=2