Question

How do you find the derivative of `sin^-1(x)`?

Answer 1

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

Explanation:

To find derivative of `sin^(-1)x`, we use the concept of function of a function.

Let `y=sin^(-1)x`, then `x=siny`

Taking derivatives of both sides, we get

`1=cosy.dy/dx` or `dy/dx=1/cosy`

But `cosy=sqrt(1-sin^2y)=sqrt(1-x^2)`

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