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

1 Answer
Oct 10, 2014

The derivative for $y = f \left(x\right) - g \left(x\right)$ works the same way as the derivative of $y = f \left(x\right) + g \left(x\right)$.

$y = f \left(x\right) - g \left(x\right) \implies \frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) - g ' \left(x\right)$

The quick proof is:
$y = f \left(x\right) - g \left(x\right) = f \left(x\right) + \left(- 1\right) g \left(x\right)$
Using the sum rule and the constant rule:
$\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) + \left(- 1\right) g ' \left(x\right) = f ' \left(x\right) - g ' \left(x\right)$.