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Question Number 22232 by tapan das last updated on 13/Oct/17

$$\mathrm{find}\frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{where}{\sin }^{-1}\left(\frac{\mathrm{x}}{\mathrm{y}}\right)=\mathrm{x}+\mathrm{y}$$

Answered by ajfour last updated on 13/Oct/17

$$x=y\sin (x+y)$$$$1=\frac{dy}{dx}\sin (x+y)+y(1+\frac{dy}{dx})\cos (x+y)$$$$\frac{dy}{dx}[\sin (x+y)+y\cos (x+y)]=$$$$1-y\cos (x+y)$$$$\frac{dy}{dx}=\frac{1-y\cos (x+y)}{\sin (x+y)+y\cos (x+y)}.$$

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