Calculus Course/Differentiation

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Derivative[edit | edit source]

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

Formula[edit | edit source]

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 | edit source]

General Rules[edit | edit source]

Powers and Polynomials[edit | edit source]

Trigonometric Functions[edit | edit source]

Exponential and Logarithmic Functions[edit | edit source]

Inverse Trigonometric Functions[edit | edit source]

Hyperbolic and Inverse Hyperbolic Functions[edit | edit source]

Reference[edit | edit source]

  1. Derivative
  2. Table_of_derivatives