Differentiate sin and its inverse

Calculus Level 3

For any real number π2<x<π\dfrac{\pi}{2}< x < \pi evaluate the following:-
ddx(sin1(sin(x)))\dfrac{d}{dx} \left({\sin}^{-1}\left(\sin\left(x\right)\right)\right)

Definitions used:

  • sin1(x)\sin^{-1}(x) is the arcsine function which gives the unique angle θx[π2,π2]\theta_x\in \left[\dfrac{-\pi}{2},\dfrac{\pi}{2}\right] such that sin(θx)=x\sin(\theta_x)=x
×

Problem Loading...

Note Loading...

Set Loading...