Talk:Sum rule in differentiation

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i think the math in this artcile should be formatted corectly... only problem is i don't know how to do it

add concrete examples and references[edit]

can we add concrete examples to the calc pages. at least two for each concept to make them useful to the average user? And this page still needs references. I will add them but Im new so I will need a little help formatting them. aharon42 (talk) 13:15, 6 September 2008 (UTC)

The actual proof?[edit]

Consider we differentiate this function y = u + v, where u and v are functions.

I let u = f(x) and v = g(x).

y = f(x) + g(x)

dy/dx = lim{m→0} [f(x+m)+g(x+m)-(f(x)+g(x))]/m

= lim{m→0} [f(x+m)-f(x)+g(x+m)-g(x)]/m

= lim{m→0} [(f(x+m)-f(x))/m+(g(x+m)-g(x))/m]

= f'(x) + g'(x)

= du/dx + dv/dx

This gives the clear proof of this without the use of the "∆x division". Garygoh884 (talk) 10:57, 25 May 2011 (UTC)