Question

What is the derivative of this function `y=sin^-1sqrtx`?

Answer 1

`dy/dx= 1/(2sqrt(1-x)sqrt(x)`

Explanation:

`y =sin^-1 sqrtx`

Applying the standard differential and the chain rule

`dy/dx= 1/sqrt(1-(sqrtx)^2) * 1/2x^(-1/2)`

`= 1/(sqrt(1-x)* 2sqrt(x)`

`= 1/(2sqrt(1-x)sqrt(x)`