# Differentiate sin and its inverse

Calculus Level 3

For any real number $$\dfrac{\pi}{2}< x < \pi$$ evaluate the following:-
$\dfrac{d}{dx} \left({\sin}^{-1}\left(\sin\left(x\right)\right)\right)$

Definitions used:

• $$\sin^{-1}(x)$$ is the arcsine function which gives the unique angle $$\theta_x\in \left[\dfrac{-\pi}{2},\dfrac{\pi}{2}\right]$$ such that $$\sin(\theta_x)=x$$
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