Find the derivative of sin⁻¹x with respect to x assuming it to exist.

Given:

Function: sin^-1(x)

Concept used:

The derivative of the inverse sine function, with respect to x is found using the chain rule. 

d/dx(sin^-1x) = 1 / √(1 - x²)

Calculation:

Applying the formula for the derivative:
  
d/dx(sin^-1x) = 1 / √(1 - x²)

⇒ d/dx(sin^-1x) = 1 / √(1 - x²)

∴ The derivative of sin^-1(x) with respect to x is \(\rm\frac{1}{\sqrt{1−x^2}}\)