Math Help - Derivatives

This section of Math Help online helps with derivatives.

What is the definition of derivatives?

Derivatives or differential coefficient for a function f(x) at the argument x the limit of the difference quotient

as the increment     tens to 0.

For functions of a single variable if the left and right hand limits exist ands are equal it is the gradient of the curse at x and is the limit of the gradient of the chord joining the point (x , f(x)) and (x+  , f(x+)).

   is the limit of      as Q approaches P.

The function of x defined as the is limit for each argument x is the first derivative of y = f(x); it is the rate of change of the value of the function with respect to the independent variable, and is written:

,       f ' (x), or        D _x f(x)

while the ratio of differences of which this is the limit is written .

The process of extracting the derivative is called differentiation. For example the first derivative of ax ⁿ is anx ^n-1 . The second derivative is the first derivative of the first derivative and is written: