Quotient Rule

Reference > Calculus: Differentiation

Description
\[(\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}\]
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
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