Calculus Course/Differentiation

Derivative Edit

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

Formula Edit

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 Derivative Edit

General Rules Edit





Powers and Polynomials Edit







Trigonometric Functions Edit







Exponential and Logarithmic Functions Edit







Inverse Trigonometric Functions Edit







Hyperbolic and Inverse Hyperbolic Functions Edit


Reference Edit

  1. Derivative
  2. Table_of_derivatives