We have realized a 76 MHz white-light differential transmission spectroscopy system. The technique employs a Ti:sapphire laser oscillator and a tapered fiber to generate a white-light continuum spanning almost the full visible to near-infrared spectral range. Using acousto-optical modulation and subsequent lock-in detection, transient relative transmission changes as small as 10(-5) are detected. The method is applied to study the ultrafast gain dynamics of the active layer of a vertical-external-cavity surface-emitting laser based on a multiple-quantum-well structure.