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 \(\sin(\theta_x)=x\)
by
Ashish Siva