Помогите решить предел

lim x->0 [ (e^x-1) / ln (1+2x) ]

Lim x->0 [ (e^x-1) / ln (1+2x) ] = lim x->0 [ (-1+e^x) / ln (1+2x) ] =

= lim x->0 [ (d (-1+e^x)) / dx] [ (d (log (1+2x) / dx] =

= lim x->0 (1/2) * e^x (1 + 2x) = (1/2) * (lim x->0 (e^x) * lim x->0 (1+2x)) =

= (1/2) * (e^ (lim x->0 (x) * (lim x->0 (1+2x)) = (1/2) * (lim x->0 (1+2x)) = 1/2