If y=sqrt{(x-sin x)+sqrt{(x-sin x)+sqrt{(x-si | vedclass

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Question

(A) Given the expression $y=\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\ldots}}}$.We can rewrite this as $y=\sqrt{(x-\sin x)+y}$.Squaring both

Vedclass · Accepted Answer

$\frac{1-\cos x}{2y-1}$

Vedclass · Answer

(A) Given the expression $y=\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\ldots}}}$.We can rewrite this as $y=\sqrt{(x-\sin x)+y}$.Squaring both sides,we get $y^2 = x - \sin x + y$.Differentiating both sides with respect to $x$,we get $2y \frac{dy}{dx} = 1 - \cos x + \frac{dy}{dx}$.Rearranging the terms to solve for $\frac{dy}{dx}$,we have $2y \frac{dy}{dx} - \frac{dy}{dx} = 1 - \cos x$.Factoring out $\frac{dy}{dx}$,we get $\frac{dy}{dx}(2y-1) = 1 - \cos x$.Therefore,$\frac{dy}{dx} = \frac{1-\cos x}{2y-1}$.

If $y=\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\sqrt{(x-\sin x) \ldots}}}$,then $\frac{dy}{dx}=$

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