Differentiate the function $\cos^{-1}(\sin x)$ with respect to $x$.

$-1$

The correct answer is Option (2) → $-1$ ##

Let $f(x) = \cos^{-1}(\sin x)$. Observe that this function is defined for all real numbers.

We may rewrite this function as

$f(x) = \cos^{-1}(\sin x)$

$= \cos^{-1} \left[ \cos \left( \frac{\pi}{2} - x \right) \right]$

$= \frac{\pi}{2} – x$

Thus, $f'(x) = -1$