This rule is for when you can split your function into one sub-function divided by another sub-function. If the two sub- functions are u and v:

_{}

Sponsored Links

Then:

_{}

Make sure you have v representing the sub-function on the bottom of the fraction, otherwise this rule won’t work. Here’s a sample question:

Find the derivative of |

Solution |

Firstly: Let u = 5x Let
v = 6x Which gives: Then: |

When you get a derivative question, your first decision should be which rule to use. You can then write your ‘u’s etc. out so they are easy to use:

_{}

_{}

_{}

_{}

Some students find it easier to just remember the product rule, and not worry about the quotient rule – any quotient rule problem can be turned into a product rule. For instance, the last example could be converted into a product rule problem by changing the function to:

_{}

_{}^{ }is really _{}. When we change
it from dividing to multiplying, we change its power from 1 to –1. In effect
we are moving it from the denominator to the numerator – the sign of the power
always changes when we do this.