# What is the derivative of x?

Oct 1, 2014

We can use the difference quotient or the power rule.

Lets use the Power Rule first.

$f \left(x\right) = x = {x}^{1}$

$f ' \left(x\right) = 1 {x}^{1 - 1} = 1 {x}^{0} = 1 \cdot 1 = 1$

Difference quotient

${\lim}_{h \to 0} = \frac{f \left(x + h\right) - f \left(x\right)}{h} = \frac{x + h - x}{h} = \frac{h}{h} = 1$

Also note that $f \left(x\right) = x$ is a linear equation, $y = 1 x + b$. The slope of this line is also 1.