Differentiation is often how many students are introduced to calculus. Its lengthy list of formulae and methods and rules are almost intimidating and it helps to have them collectively in one place for reference.
This list is aimed at serving that purpose: it is not a guide or explanation, but a collection of formulae and rules structured to be easy to follow and to serve as a reference sheet to look through and recollect.
It is divided into two parts: identities, or the basic derivative formulae; and rules which explain the methods of solving common differentiation forms. We refer to variables as x, y, z etc. and functions performed on those variables as f(x), g(x) etc. with , etc. being their respective derivatives. We will refer to constants as C, a or b and the exponent as e.
The following are various formulae used to compute the derivative (i.e. to differentiate) a function. These can be derived from first principles, although we will not be doing that here.
Reading this table is simple: for instance, at (7) we have the following:
This is simply ready as .
Inverse hyperbolic trigonometric
There are some rules when differentiating more complicated functions or functions within functions. The idea is simply to compare the function(s) at hand with the rules, see which rule the function(s) best resembles and apply that rule. To solve specific functions, we once again have to look to the list of differentiation formulae above.
These are the most commonly encountered rules and differentiation formulae in physics. If you look through our Learn section, you might find a lot of these formulae being used or referred to.
For convenience, a pdf version of this list will be made available for download soon.
Cover image by Alex.