derivació y integració exponencial

D_{x}[f(x)] = lim [h-->0][ (f(x+h)+(-1)·f(x))/(h·f(x)) ] = ( d_{x}[f(x)]/f(x) )


D_{x}[c] = 0


D_{x}[x^{n}] = (n/x)


D_{x}[e^{x}] = 1


D_{x}[a^{x}] = ln(a)


D_{x}[ln(x)] = ( 1/ln(x) )·(1/x)


D_{x}[f(x)+g(x)] = D_{x}[f(x)] + D_{x}[g(x)]


D_{x}[a·f(x)] = D_{x}[f(x)]


D_{x}[f(x)·g(x)] = D_{x}[f(x)]·g(x) + f(x)·D_{x}[g(x)]


D_{x}[ax^{2}+bx+c] = (2ax+b)/(ax^{2}+bx)


∫ [ D_{x}[f(x)] ] d[x] = ln( ∫ [ D_{x}[f(x)] ] D[x] )


e^{ ∫ [ D_{x}[f(x)] ] d[x] } = ∫ [ D_{x}[f(x)] ] D[x]


e^{∫ d[x]} = ∫ D[x] = e^{x}


e^{∫ [(n/x)] d[x]} = ∫ (n/x) D[x]
e^{ln(x^{n})} = x^{n}


e^{∫ [ ln(a) ] d[x]} = ∫ [ ln(a) ] D[x]
e^{ln(a)·x} = a^{x}


e^{∫ [ ( 1/ln(x) )·(1/x) ] d[x]} = ∫ [ ( 1/ln(x) )·(1/x) ] D[x]
e^{ln(ln(x))} = ln(x)


D_{x}[f(g(x))] = d_{g(x)}[f(g(x))]·d_{x}[g(x)]·(1/f(g(x)))


e^{∫ [ x^{n} ] d[x]} = ∫ [ x^{n} ] D[x] = e^{(1/(n+1))·x^{(n+1)}}
D_{x}[ e^{(1/(n+1))·x^{(n+1)}} ] = x^{n}