Question

Find the derivative of
y = arcsin(x)​

Answer 1

1 /√( 1 - x^2).

Explanation:

y = arcsin x

x = sin y

dx/dy = cos y

dy/dx = 1 / cos y

Now cos y = √( 1 - sin^2 y)

but sin y = x so

cos y = √( 1 - x^2).

So dy/dx = 1 / √( 1 - x^2).

Answer 2

f'(x)=
`\frac{1}{\sqrt{1-x^(2) } }`

Explanation:

As khown the derivative of arcsin(x) is;

f'(x)=
`\frac{1}{\sqrt{1-x^(2) } }`