If y=sqrt{cosh x+sqrt{cosh x+dots}},then frac | vedclass

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Question

(A) Given the equation $y = \sqrt{\cosh x + y}$.Squaring both sides,we get $y^2 = \cosh x + y$.Differentiating both sides with respect to $x$,we have

Vedclass · Accepted Answer

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

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(A) Given the equation $y = \sqrt{\cosh x + y}$.Squaring both sides,we get $y^2 = \cosh x + y$.Differentiating both sides with respect to $x$,we have $\frac{d}{dx}(y^2) = \frac{d}{dx}(\cosh x + y)$.This simplifies to $2y \frac{dy}{dx} = \sinh x + \frac{dy}{dx}$.Rearranging the terms to isolate $\frac{dy}{dx}$,we get $2y \frac{dy}{dx} - \frac{dy}{dx} = \sinh x$.Factoring out $\frac{dy}{dx}$,we have $\frac{dy}{dx}(2y - 1) = \sinh x$.Therefore,$\frac{dy}{dx} = \frac{\sinh x}{2y - 1}$.

If $y=\sqrt{\cosh x+\sqrt{\cosh x+\dots}}$,then $\frac{d y}{d x}=$

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