The Difference Rule for Derivatives

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The derivative of the difference of functions is equal to the difference of the derivatives of the functions.

[f(x)-g(x)]'

= \lim\limits_{\Delta x \to0} \dfrac{[f(x+\Delta x )-g(x+\Delta x )]-[f(x)-g(x)]}{\Delta x }

= \lim\limits_{\Delta x \to0} \dfrac{f(x+\Delta x )-f(x)}{\Delta x } - \lim\limits_{\Delta x \to0} \dfrac{g(x+\Delta x )-g(x)}{\Delta x }

= f'(x) - g'(x)

or

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