Nth Deriv. Proof Addition

Murk

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Feb 23, 2010
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\(\displaystyle f^{(n)}(a), g^{(n)}(a)\) exists. Prove \(\displaystyle (f+g)^{(n)}(a) = f^{(n)}(a) + g^{(n)}(a)\). How do I even begin to start to prove or disprove this? The only thing I see in my book is that \(\displaystyle (f^n)'(c) = n(f(c))^{n-1}f'(c)\)
 
Are you supposed to use the limit definition? You cannot use what you see in your book. The superscripts \(\displaystyle ^n\) and \(\displaystyle ^{(n)}\) are ENTIRELY DIFFERENT.
 
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