Quotient Rule

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Using quotient rule, d/dx[x/sin(x)] equals

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1. **Rule Statement**: $\frac{d}{dx}(\frac{u}{v}) = \frac{v u' - u v'}{v^2}$.
2. **Identify Functions**: $u = x$ (numerator), $v = \sin x$ (denominator).
3. **Derivatives**: $u' = 1$, $v' = \cos x$.
4. **Application**:
   - $\frac{d}{dx}(\frac{x}{\sin x}) = \frac{(\sin x)(1) - (x)(\cos x)}{(\sin x)^2}$
   - $= \frac{\sin x - x \cos x}{\sin^2 x}$.

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Quotient Rule

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