càlcul diferencial y integral linialitat

d[ f(x)+g(x) ] = ( f(x+h)+g(x+h) )+(-1)·( f(x)+g(x) )

d[ f(x)+g(x) ] = ( f(x+h)+(-1)·f(x) )+( g(x+h)+(-1)·g(x) ) = d[f(x)]+d[g(x)]

d[ s·f(x) ] = ( s·f(x+h) )+(-1)·( s·f(x) ) = s·( f(x+h)+(-1)·f(x) ) = s·d[f(x)]

d_{x}[ int[ f(x)+g(x) ] d[x] ] = f(x)+g(x) = d_{x}[ int[f(x)] d[x] ]+d_{x}[ int[g(x)] d[x] ]

d_{x}[ int[ f(x)+g(x) ] d[x] ] = d_{x}[ int[f(x)] d[x]+int[g(x)] d[x] ]

int[ d_{x}[ int[ f(x)+g(x) ] d[x] ] ] d[x] = int[ d_{x}[ int[f(x)] d[x]+int[g(x)] d[x] ] ] d[x]

int[ f(x)+g(x) ] d[x] = int[f(x)] d[x]+int[g(x)] d[x]

d_{x}[ int[ s·f(x) ] d[x] ] = s·f(x) = s·d_{x}[ int[f(x)] d[x] ]

d_{x}[ int[ s·f(x) ] d[x] ] = d_{x}[ s·int[f(x)] d[x] ]

int[ d_{x}[ int[ s·f(x) ] d[x] ] ] d[x] = int[ d_{x}[ s·int[f(x)] d[x] ] ] d[x]

int[ s·f(x) ] d[x] = s·int[f(x)] d[x]

d[f(x)·g(x)] = (1/2)·( ( 2·f(x+h)·g(x+h) )+(-1)·( 2·f(x)·g(x) ) )

d[f(x)·g(x)] = (1/2)·( ( f(x+h)+(-1)·f(x) )·( g(x+h)+g(x) )+( f(x+h)+f(x) )·( g(x+h)+(-1)·g(x) ) )

d[f(x)·g(x)] = d[f(x)]·g(x)+f(x)·d[g(x)]

f(x)·g(x) = f(x) [o(x)o] int[g(x)] d[x]+int[f(x)] d[x] [o(x)o] g(x)

x^{n} = x^{(n/2)} [o(x)o] ( 4/(n+2) )·x^{((n+2)/2)}