Differentiate the following function with respect to `x :` `sin^(-1){(x+sqrt(1-x^2))/(sqrt(2))},-1

Explanation

Let `y = sin^-1{(x+sqrt(1-x^2))/sqrt2}`

Let `x = sin t`

Then,

`y = sin^-1{(sint+sqrt(1-sin^2t))/sqrt2}`

`=>y = sin^-1{(sint+cost)/sqrt2}`

`=> y = sin^-1{(sint*1/sqrt2+cost*1/sqrt2)}`

`=> y = sin^-1{(sintcospi/4+costsinpi/4)}`

As, `sinAcosB+cosAsinB = sin(A+B)`

...