Calculus Course/Differentiation

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Contents

DerivativeEdit

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

FormulaEdit

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

 
 
 
 
 
 
 
 
 
 
 
 

ReferenceEdit