# How do you find the derivative of y = f(x) - g(x)?

The derivative for $y = f \left(x\right) - g \left(x\right)$ works the same way as the derivative of $y = f \left(x\right) + g \left(x\right)$.
$y = f \left(x\right) - g \left(x\right) \implies \frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) - g ' \left(x\right)$
$y = f \left(x\right) - g \left(x\right) = f \left(x\right) + \left(- 1\right) g \left(x\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) + \left(- 1\right) g ' \left(x\right) = f ' \left(x\right) - g ' \left(x\right)$.