Question : If y=1/(1-x^2)^(1/2) then find dy/dxSolution :Given \[y=\frac{1}{\sqrt{1-x^2}}\]is a rational function.So to find it’s derivative, we shall use formula of derivative for a rational function\[\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}\]Where \[u =1 , v =\sqrt{1-x^2}\]then \[\frac{dy}{dx}=\frac{d}{dx}(\frac{u}{v})=\frac{\sqrt{1-x^2}\frac{d(1)}{dx}-1\frac{d(\sqrt{1-x^2})}{dx}}{1-x^2}\]\[\frac{dy}{dx}=\frac{d}{dx}(\frac{u}{v})=\frac{\sqrt{1-x^2}*0-1*\left(-\frac{x}{\sqrt{1-x^2}}\right)}{1-x^2}\]\[\frac{dy}{dx}=\frac{x}{\sqrt{1-x^2}}\]
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