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y-sinh-1-sin-x-dy-dx-




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

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