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English
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Quotient RuleDescription \[(\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}\] |
Examples \[\frac{d}{dx} \frac{\sin{x}}{{x}^{2}}\] 1 Use Quotient Rule to find the derivative of \(\frac{\sin{x}}{{x}^{2}}\). The quotient rule states that \((\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}\). \[\frac{{x}^{2}(\frac{d}{dx} \sin{x})-\sin{x}(\frac{d}{dx} {x}^{2})}{{x}^{4}}\] 2 Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\). \[\frac{{x}^{2}\cos{x}-\sin{x}(\frac{d}{dx} {x}^{2})}{{x}^{4}}\] 3 Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\). \[\frac{{x}^{2}\cos{x}-2x\sin{x}}{{x}^{4}}\] Done  |
See Also - Sum Rule |