Question Number 113196 by bobhans last updated on 11/Sep/20
$$\:\mathrm{y}\:=\:\mathrm{sinh}\:^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)\:,\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=? \\ $$
Answered by MJS_new last updated on 11/Sep/20
$$\left({f}\left({g}\left({x}\right)\right)'={g}'\left({x}\right)×{f}'\left({g}\left({x}\right)\right)\right. \\ $$$$\left(\mathrm{sinh}^{−\mathrm{1}} \:\mathrm{sin}\:{x}\right)'=\mathrm{cos}\:{x}\:×\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:{x}}} \\ $$