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Question Number 164747 by mathlove last updated on 21/Jan/22

$$faind\frac{dy}{dx}$$$${sin}^{-1}\left(xy\right)={csc}^{-1}(x-y)$$

Answered by mahdipoor last updated on 21/Jan/22

$${sin}^{-1}\left(xy\right)={sin}^{-1}\left(\frac{1}{x-y}\right)\Rightarrow$$$$xy=\frac{1}{x-y}\Rightarrow y+x\frac{dy}{dx}=\frac{1-\frac{dy}{dx}}{{(x-y)}^2}\Rightarrow$$$$\frac{dy}{dx}=\frac{1-y{(x-y)}^2}{1+x{(x-y)}^2}$$

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