Difference between revisions of "Matrix multiplication"

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Let <math> h(x) = f(x) + g(x) </math>. For all <math> x </math> near <math> a </math> we have <math> h(x) = f(x) + g(x)\approx = \left[ f(a) + f'(a) (x-a) \right] + \left[ g(a) + g'(a) (x-a) \right] = \left[f(a) +g(a)\rigth]+ \left[f'(a) +g'(a)\right](x-a) </math>.  Since <math> h(a) = f(a) +g(a) </math>, we obtain <math> h(x)\approx h(a) + {\color{red}\left[ f'(a)+g'(a)\right]} (x-a) </math>. Comparing it with <math> h(x)\approx h(a) + {\color{red} h'(a)} (x-a)</math> we conclude that <math> h'(a) = f'(a)+g'(a)</math>, or (replacing <math>a</math> with an arbitrary variable):
 
  
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<math> \boxed{(f(x)+g(x))' = f'(x)+g'(x)} </math>
 

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