Quotient Rule

Let \(u\) and \(v\) be differentiable functions of \(x\). Choose the rule that matches the way the two functions are combined.

Quotient rule

\[\frac{\mathrm{d}}{\mathrm{d}x}\left(\frac{u}{v}\right)=\frac{v\frac{\mathrm{d}u}{\mathrm{d}x}-u\frac{\mathrm{d}v}{\mathrm{d}x}}{v^2},\qquad v\ne0\]

Keep the order in the numerator: denominator times derivative of numerator, minus numerator times derivative of denominator.