Calculus Course/Differentiation

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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