Derivative functions > Finding the derivative
1234Finding the derivative

## Theory

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

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 $f\left(x\right)=u\left(x\right)±v\left(x\right)$ then $f\text{'}\left(x\right)=u\text{'}\left(x\right)±v\text{'}\left(x\right)$.