Here's a handy summary of the differentiation rules you'll frequently use.
The differentiation rule for the product of two functions: • For examples of the Product Rule,
visit our Calculating
Derivatives: Problems & Solutions page!
The differentiation rule for the quotient of two functions: Many students remember the quotient rule by
thinking of the numerator as "hi," the demoninator as "lo," the derivative
as "d," and then singing
"lo d-hi minus hi d-lo over lo-lo"
• For examples of the Quotient Rule: Calculating
Derivatives: Problems & Solutions.
The differentiation rule for the composition of two functions:
Alternatively, if we write
and then Informally: •
For many examples of the Chain Rule: Chain Rule: Problems &
One quick example: Consider To find the derivative,
think something like: "The function is a bunch of stuff to the 7th power.
So the derivative is 7 times that same stuff to the 6th power, times the
derivative of that stuff."
Note: You'd never actually write out "stuff = ...." Instead just
hold in your head what that "stuff" is, and proceed to write down the
Tip: You can differentiate any function, for free, using Wolfram
WolframAlpha's Online Derivative