Differentiation rules > Differentiation rules
123456Differentiation rules

## Theory

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

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

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.