# How do you find the derivative of x/2?

May 15, 2016

Use the facts that $\frac{x}{2} = \frac{1}{2} x$ and $\frac{d}{\mathrm{dx}} \left(k x\right) = k$ to get $\frac{d}{\mathrm{dx}} \left(\frac{x}{2}\right) = \frac{1}{2}$

#### Explanation:

$\frac{d}{\mathrm{dx}} \left(\frac{x}{2}\right) = \frac{d}{\mathrm{dx}} \left(\frac{1}{2} x\right) = \frac{1}{2} \frac{d}{\mathrm{dx}} \left(x\right) = \frac{1}{2} \left(1\right) = \frac{1}{2}$

If you prefer to use the quotient rule it looks like this:

$\frac{d}{\mathrm{dx}} \left(\frac{x}{2}\right) = \frac{\frac{d}{\mathrm{dx}} \left(x\right) \cdot 2 - x \frac{d}{\mathrm{dx}} \left(2\right)}{2} ^ 2$

$= \frac{1 \cdot 2 - x \cdot \left(0\right)}{4} = \frac{2}{4} = \frac{1}{2}$