# How do you find the derivative of  x?

Jul 30, 2016

Power rule or limit definition.

#### Explanation:

The power rule gives it to you straight away:

$\frac{d}{\mathrm{dx}} x = \frac{d}{\mathrm{dx}} {x}^{1} = 1 \cdot {x}^{0} = 1$

Alternatively using the limit definition.

Let $f \left(x\right) = x$

$f ' \left(a\right) = {\lim}_{h \to 0} \frac{f \left(a + h\right) - f \left(a\right)}{h}$

$= {\lim}_{h \to 0} \frac{\left(a + h\right) - a}{h}$

$= {\lim}_{h \to 0} \frac{h}{h}$

$= {\lim}_{h \to 0} 1$

$= 1$