A measurement of the derivative (d ln F_2 / d ln x)_Q^2 = -lambda(x,Q^2) of the proton structure function F_2 is presented in the low-x domain of deeply inelastic positron-proton scattering. For 0.01 > x > 5 * 10^-5 and Q^2 > 1.5 GeV^2, lambda(x,Q^2) is found to be independent of x and to rise linearly with ln Q^2.