Calculus Course/Differentiation

< Calculus Course



A derivative is a mathematical operation to find the rate of change of a function.


For a non linear function   . The rate of change of   correspond to change of   is equal to the ratio of change in   over change in  


Then the Derivative of the function is defined as


but the derivative must exist uniquely at the point x. Seemingly well-behaved functions might not have derivatives at certain points. As examples,   has no derivative at   ;   has two possible results at   (-1 for any value for which   and 1 for any value for which  ) On the other side, a function might have no value at   but a derivative of   , for example   at   . The function is undefined at   , but the derivative is 0 at   as for any other value of   .

Practically all rules result, directly or indirectly, from a generalized treatment of the function.

Table of DerivativeEdit

General RulesEdit





Powers and PolynomialsEdit







Trigonometric FunctionsEdit







Exponential and Logarithmic FunctionsEdit







Inverse Trigonometric FunctionsEdit







Hyperbolic and Inverse Hyperbolic FunctionsEdit