Higher Order Derivatives

If the derivative of a function (the first derivative, f'(x)) is differentiated, a new function is obtained called the second derivative, f''(x).

If this function is differentiated again, a third derivative, f'''(x), is obtained.

If the third derivative, f'''(x), is differntiated, the fourth derivative, f'v(x), is obtained. This process can continue and these resultant functions are referred to as higher order derivatives.

Examples

Calculate the 1st, 2nd, 3rd and 4th derivatives of:

Function

First Derivative

Second Derivative

Third Derivative

Fourth Derivative


nth Derivative

A general formula for all of the successive derivatives exists. This formula is called the nth derivative, f'n(x).


Examples

Calculate the nth derivative of:

Function

First Derivative

Second Derivative

Third Derivative

ect.

Nth Derivative Formula





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