We measure the second- and third-order dispersion coefficients, d(2)k/domega(2) and d(3)k/domega(3), of water for wavelengths from 0.45 to 1.3 mum using a Michelson white-light interferometer. In this interval, the second-order dispersion ranges from 0.068 to -0.1 fs(2)/mum, and the third-order dispersion ranges from 0.048 to 1.18 fs(3)/mum. We observe an oscillation in d(2)k/domega(2) near 1.1 mum that is due to water absorption features near that wavelength. From the dispersion coefficients, derivatives of the index of refraction of water are calculated and compared with available equations. These measured values of d(2)n/dlambda(2) and d(3)n/dlambda(3) should be useful in the evaluation and improvement of existing equations for n(lambda) in water.