The Sum Rule For Derivatives
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The derivative of the sum of functions is the same as the sum 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