If $y = \sin^{-1}(x)$, then $\dfrac{dy}{dx}$ equals:

Step-by-step Solution:

Let $y = \sin^{-1}(x)$

This means $\sin(y) = x$

Differentiating both sides w.r.t. $x$:

$$\cos(y) \cdot \frac{dy}{dx} = 1$$

$$\frac{dy}{dx} = \frac{1}{\cos(y)}$$

Since $\sin(y) = x$, we have $\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - x^2}$

$$\boxed{\frac{dy}{dx} = \frac{1}{\sqrt{1-x^2}}}$$

Hence, Option A is correct.