How do you find the derivative of  x/2?

Aug 31, 2016

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

Explanation:

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

If you really want to use the quotient rule, it's

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

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

$= \frac{2}{4} = \frac{1}{2}$