List of formulae for differentiation


Below is the list of formulae for differentiation, but as an exercise, you should also try to deduce the following formulae using the first principle, which will help you greatly in grasping the core of differentiation.


List of common rules:



Please really note these rules by heart. Here I will particularly introduce the use of the third rule, the chain rule, as it is the most difficult to grasp.



Some basic rules (non-trigonometric formulae):



A particularly useful method using natural logarithm, known as logarithmic differentiation:



The derivative of exponential function is actually derived using the same way. It’s also used when the function is ultra-complicated, with easily differentiable factors multiplying or dividing or even be squared or square-rooted.


Other formulae (involving [normal] trigonometric functions):




Proofs are left as exercise.


The formulae below are additional, as these functions are not likely to be used, unless when it is in integration. But it will be good if you want to learn more about the derivation of those formulae.



Here are more:



The last three functions are less likely to be expressed in arccsc, arcsec, or arccot form.


Please note these by heart!