Differentiation rules > Differentiation rules

The derivative of a function
$y=f\left(x\right)$ can be found by letting
$h$ go to
$0$ in the difference quotient:

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

Normally you do not find the derivative this way, but by using differentiation rules of which you already know some.

Differentiation rule 1 (power rule):

If
$f\left(x\right)=c{x}^{n}$ then
$f\prime \left(x\right)=nc{x}^{n-1}$ for any
$c$ and for integer positive
$n$.

Differentiation rule 2 (rule for constants):

If
$f\left(x\right)=c$ then
$f\prime \left(x\right)=0$.

Differentiation rule 3 (sum rule):

If
$f\left(x\right)=u\left(x\right)\pm v\left(x\right)$ then
$f\prime \left(x\right)=u\prime \left(x\right)\pm v\prime \left(x\right)$.

These differentiation rules are useful when computing the slope of the graph of a function that consists of the sum (or difference) of power functions with positive integer exponents. When dealing with other functions, other differentiation rules are needed.