How do you find the derivative of the function f(x)=1/2x-1/3?

Dec 12, 2016

We wouldn't use the power rule for this function.

We would, however, use the rule of multiplication by constant.

In general:

$\frac{d}{\mathrm{dx}} \left(c f\right) = c \cdot \frac{d}{\mathrm{dx}} f$

Also, keep in mind that:

$\frac{d}{\mathrm{dx}} \left(c\right) = 0$

Similarly, your function in these terms would look like:

$f \left(x\right) = {c}_{1} f - {c}_{2}$

Where:

${c}_{1} = \frac{1}{2}$ and ${c}_{2} = \frac{1}{3}$

$\therefore \frac{d}{\mathrm{dx}} \left(\frac{1}{2} x - \frac{1}{3}\right) = \frac{1}{2} \cdot 1 - 0$

$= \frac{1}{2}$