If y = sqrt {frac{(x - a)(x - b)}{(x - c)(x - | vedclass

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Question

(A) Given $y = \sqrt {\frac{(x - a)(x - b)}{(x - c)(x - d)}} $.Taking the natural logarithm on both sides:$\log y = \frac{1}{2} [\log (x - a) + \log (

Vedclass · Accepted Answer

$\frac{y}{2}\left[ \frac{1}{x - a} + \frac{1}{x - b} - \frac{1}{x - c} - \frac{1}{x - d} \right]$

Vedclass · Answer

(A) Given $y = \sqrt {\frac{(x - a)(x - b)}{(x - c)(x - d)}} $.Taking the natural logarithm on both sides:$\log y = \frac{1}{2} [\log (x - a) + \log (x - b) - \log (x - c) - \log (x - d)]$Now,differentiating both sides with respect to $x$:$\frac{1}{y} \frac{dy}{dx} = \frac{1}{2} \left[ \frac{1}{x - a} + \frac{1}{x - b} - \frac{1}{x - c} - \frac{1}{x - d} \right]$Multiplying both sides by $y$:$\frac{dy}{dx} = \frac{y}{2} \left[ \frac{1}{x - a} + \frac{1}{x - b} - \frac{1}{x - c} - \frac{1}{x - d} \right]$Thus,the correct option is $A$.

If $y = \sqrt {\frac{(x - a)(x - b)}{(x - c)(x - d)}} $,then $\frac{dy}{dx} = $

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