Difference between revisions of "Quotient rule"
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m (Oops, mixed the positions up (not critical, but makes it harder to memorize).) |
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Alternatively, in prime notation, it can be written as: | Alternatively, in prime notation, it can be written as: | ||
| − | <math>\left(\frac{u}{v}\right)' = \frac{ | + | <math>\left(\frac{u}{v}\right)' = \frac{u'v - v'u}{v^2}</math> |
It is easily remembered by the rhyme "Low 'D' High minus High 'D' Low, draw the line, and square below" (the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared). | It is easily remembered by the rhyme "Low 'D' High minus High 'D' Low, draw the line, and square below" (the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared). | ||
Revision as of 13:31, January 6, 2013
| <math>\frac{d}{dx} \sin x=?\,</math> | This article/section deals with mathematical concepts appropriate for late high school or early college. |
The Quotient Rule is a rule in calculus pertaining to the derivative of a variable or function divided by another. It can be written as follows:
<math>\frac{d}{dx} \left(\frac{u}{v}\right) = \frac{v \left(\frac{du}{dx}\right) - u \left(\frac{dv}{dx}\right)}{v^2}</math>
Alternatively, in prime notation, it can be written as:
<math>\left(\frac{u}{v}\right)' = \frac{u'v - v'u}{v^2}</math>
It is easily remembered by the rhyme "Low 'D' High minus High 'D' Low, draw the line, and square below" (the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared).