# How do you differentiate f(x)=x+x-2x using the sum rule?

Dec 19, 2015

According to the sum rule,

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[x\right] + \frac{d}{\mathrm{dx}} \left[x\right] - \frac{d}{\mathrm{dx}} \left[2 x\right]$

$\frac{d}{\mathrm{dx}} \left[x\right] = 1$

$\frac{d}{\mathrm{dx}} \left[2 x\right] = 2$

Thus,

f'(x)=1+1-2=color(red)(0

This should be fairly obvious because $f \left(x\right)$ can be simplified from the beginning to find that $f \left(x\right) = 0$, so $f ' \left(x\right) = 0$ as well.