derivades

proposició:
si ( M [< x [< 2M & f(x)=ln(x^{n}) ) ==> n [< d_{x}[f(x)]·2M [< 2n
d_{x}[f(x)]=(n/x)
(n/2M) [< d_{x}[f(x)] [< (2n/2M)


proposició:
si ( M [< x [< 2M & f(x)=(n/x) ) ==> n [< d_{xx}[f(x)]·4M^{3} [< 8n
d_{xx}[f(x)]=(2n/x^{3})
(n/4M^{3}) [< d_{xx}[f(x)] [< (8n/4M^{3})


proposició:
si ( M [< x [< 2M & f(x)=(n/x^{2}) ) ==> 3n [< d_{xx}[f(x)]·8M^{4} [< 48n
d_{xx}[f(x)]=(6n/x^{4})
(3n/8M^{4}) [< d_{xx}[f(x)] [< (48n/8M^{4})


proposició:
si ( M [< x [< 2M & f(x)=(n/x^{3}) ) ==> 3n [< d_{xx}[f(x)]·8M^{5} [< 96n
d_{xx}[f(x)]=(12n/x^{5})
(3n/8M^{5}) [< d_{xx}[f(x)] [< (96n/8M^{5})