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