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)
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