THE DERIVATIVES OF THE NATURAL LOG - Homepage for Miles Mathis science site
The derivative for the natural log is currently found by this method: dln(x)/dx = lim d→0 [ln(x+d) - ln(x)]/d = lim ln[(x+d)/x]/d = lim(1/d) ln(1 + d/x) = lim[ln(1 + d/x) 1/d] Set u=d/x and substitute: lim u→0 [ ln (1 + u) 1/ux] = 1/x ln [lim u→0 (1 + u) ...