Question

what is the derivative of sin inverse function​

Answer 1

$\Huge\pmb{Answer}$

The derivative of the inverse-sine function is actually quite a nice demonstration of what we call implicit differentiation.

y=arcsin(x)

Now — we take the sin of both sides to get:

sin(y)=sin(arcsin(x))=x

Now we differentiate, to get:

d/dxsin(y)=1

Answer 2

$\Huge\pmb{Answer}$

The derivative of the inverse-sine function is actually quite a nice demonstration of what we call implicit differentiation.

y=arcsin(x)

Now — we take the sin of both sides to get:

sin(y)=sin(arcsin(x))=x

Now we differentiate, to get:

d/dxsin(y)=1