The temporal dependence of the 14.7 nm Ni-like Pd ion x-ray laser is measured as a function of the laser drive conditions with a fast sub-picosecond x-ray streak camera. The chirped pulse amplification laser beam that pumps the inversion process is varied from 0.5 - 27 ps (FWHM) to determine the effect on the x-ray laser pulse duration. The average x-ray laser pulse duration varies by a relatively small factor of 2.5 times from 3.6 ps to 8.1 ps with travelling wave (TW) irradiation conditions. Slightly shorter pulse durations approaching 2 ps are observed with the x-ray laser operating below saturation. The x-ray laser is found to be 4 - 5 times transform-limited for 6 - 13 ps laser pumping conditions.