Similar to product rule, the quotient rule is a way of differentiating the quotient, or division of functions. The quotient rule is defined as the quantity of the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared.
The Formula for the Quotient Rule
The quotient rule can be more difficult to remember because the order of functions matters. An easier way to remember it is saying "Low D High take High D Low - Cross the line and square the Low"
(1) Differentiate the quotient
We take the denominator times the derivative of the numerator (low d-high). . .
Then subtract the numerator times the derivative of the denominator ( take high d-low). . .
Divide it by the square of the denominator (cross the line and square the low)
Finally, we simplify
(2) Let's do another example. Find the derivative of
A quick glance at this may fool us into thinking it requires quotient rule because of the clear numerator and denominator. If we look closely, we can see that we can rearrange this function.
The 1⁄7 is a constant, so we can pull it in front as a coefficient and use the good old power rule to differentiate.