Find the derivative: frac{d}{dx} log (sqrt{x | vedclass

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Question

(B) Let $y = \log (\sqrt{x - a} + \sqrt{x - b})$.Applying the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \frac{1}{\sqrt{x - a} +

Vedclass · Accepted Answer

$\frac{1}{2\sqrt{(x - a)(x - b)}}$

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(B) Let $y = \log (\sqrt{x - a} + \sqrt{x - b})$.Applying the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \frac{1}{\sqrt{x - a} + \sqrt{x - b}} \cdot \frac{d}{dx}(\sqrt{x - a} + \sqrt{x - b})$$= \frac{1}{\sqrt{x - a} + \sqrt{x - b}} \cdot \left( \frac{1}{2\sqrt{x - a}} + \frac{1}{2\sqrt{x - b}} \right)$$= \frac{1}{\sqrt{x - a} + \sqrt{x - b}} \cdot \frac{1}{2} \left( \frac{\sqrt{x - b} + \sqrt{x - a}}{\sqrt{x - a}\sqrt{x - b}} \right)$$= \frac{1}{\sqrt{x - a} + \sqrt{x - b}} \cdot \frac{\sqrt{x - a} + \sqrt{x - b}}{2\sqrt{(x - a)(x - b)}}$$= \frac{1}{2\sqrt{(x - a)(x - b)}}$.

Find the derivative: $\frac{d}{dx} \log (\sqrt{x - a} + \sqrt{x - b})$

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