You are doing your homework and have the following function in front of you, for example:
You should form the first derivative and the second derivative of this. Which derivation rule can you use in such a case? Luckily you came across this explanation of the quotient rule on the internet. Your homework is saved!
Derivation rule Quotient rule – definition and application
Some functions consist of a quotient, where both the numerator and the denominator contain their own function term. To derive this type of function, you need the quotient rule. But which functions can be derived in general with the quotient rule?
Memory aid:
- mnemonic: through
- Meaning/Spoken: Denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator divided by the denominator squared.
How can you use the formula when deriving a function? time for an example.
Quotient rule derivation – application example
A fractional function can be derived using the quotient rule as follows.
Now you already know the formula of the quotient rule. But why does the quotient rule apply at all? Are you interested in the derivation of the quotient rule? Then you will find the answers in the following deepening. Feel free to skip this section if you want to go straight to the examples and tasks.
Quotient rule derivation – practice problems
At the end you can now put the knowledge you have learned to the test and solve the following exercises. Feel free to use your own formulary from school if you are allowed to use one!
Quotient Rule Derivation Exercise 1. Derivation
Since you have now dealt intensively with the topic of the quotient rule, you can solve your homework in no time.