Derivative functions > Finding the derivative

You can determine the derivative of a function
$y=f\left(x\right)$ by letting
$h$ approach to
$0$ in the difference quotient:

$\frac{\Delta y}{\Delta x}=\frac{f(x+h)-f\left(x\right)}{h}$

You can use this to set up some general rules that make it easier to determine the derivatives of a lot of functions. These are called the differentiation rules and applying these rules is called differentiating.

Differentiation rule 1 (the power rule):

The derivative of
$f\left(x\right)=c{x}^{n}$ is
$f\text{'}\left(x\right)=nc{x}^{n-1}$ for every value of
$c$ and for positive integer values of
$n$.

Differentiation rule 2 (the constant rule):

The derivative of a constant (function) is
$0$: if
$f\left(x\right)=c$ then
$f\text{'}\left(x\right)=0$.

Differentiation rule 3 (the sum rule):

The derivative of a sum (or difference) of two functions is the sum (or difference)
of the derivatives of these functions: if
$f\left(x\right)=u\left(x\right)\pm v\left(x\right)$ then
$f\text{'}\left(x\right)=u\text{'}\left(x\right)\pm v\text{'}\left(x\right)$.