If y = frac{x}{a + frac{x}{b + frac{x}{a + fr | vedclass

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Question

(A) Given the infinite continued fraction: $y = \frac{x}{a + \frac{x}{b + y}}$.Multiply both sides by $(a + \frac{x}{b + y})$: $y(a + \frac{x}{b + y})

Vedclass · Accepted Answer

$\frac{b}{ab + 2ay}$

Vedclass · Answer

(A) Given the infinite continued fraction: $y = \frac{x}{a + \frac{x}{b + y}}$.Multiply both sides by $(a + \frac{x}{b + y})$: $y(a + \frac{x}{b + y}) = x$.$ay + \frac{xy}{b + y} = x$.Multiply by $(b + y)$: $ay(b + y) + xy = x(b + y)$.$aby + ay^2 + xy = bx + xy$.$aby + ay^2 = bx$.Now,differentiate both sides with respect to $x$: $\frac{d}{dx}(aby + ay^2) = \frac{d}{dx}(bx)$.$ab \frac{dy}{dx} + 2ay \frac{dy}{dx} = b$.$\frac{dy}{dx}(ab + 2ay) = b$.Therefore,$\frac{dy}{dx} = \frac{b}{ab + 2ay}$.

If $y = \frac{x}{a + \frac{x}{b + \frac{x}{a + \frac{x}{b + \dots \infty}}}},$ then $\frac{dy}{dx} = $

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