Find the derivative: frac{d}{dx} left( frac{l | vedclass

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(B) To find the derivative of $\frac{\log x}{\sin x}$,we use the quotient rule: $\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \frac{du}{dx} - u \

Vedclass · Accepted Answer

$\frac{\frac{\sin x}{x} - \log x \cdot \cos x}{\sin^2 x}$

Vedclass · Answer

(B) To find the derivative of $\frac{\log x}{\sin x}$,we use the quotient rule: $\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2}$.Here,$u = \log x$ and $v = \sin x$.Then,$\frac{du}{dx} = \frac{1}{x}$ and $\frac{dv}{dx} = \cos x$.Applying the quotient rule:$\frac{d}{dx} \left( \frac{\log x}{\sin x} \right) = \frac{\sin x \cdot \frac{1}{x} - \log x \cdot \cos x}{(\sin x)^2}$.This simplifies to $\frac{\frac{\sin x}{x} - \log x \cdot \cos x}{\sin^2 x}$.

Find the derivative: $\frac{d}{dx} \left( \frac{\log x}{\sin x} \right)$

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