مشتق این تابع به صورت زیر محاسبه می شود:

که در آن  تابع دی گاما (Digamma function) نام دارد. nامین مشتق تابع گامای اویلر از این تابع حاصل می شود که نمایش آن به صورتهای...  است.

منابع:

Abramowitz, M. and Stegun, I. A. (Eds.). "Psi (Digamma) Function." §6.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 258-259, 1972.

Arfken, G. "Digamma and Polygamma Functions." §10.2 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 549-555, 1985.

Boros, G. and Moll, V. "The Psi Function." §10.11 in Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals. Cambridge, England: Cambridge University Press, pp. 212-215, 2004.

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. "The Function." §1.7 in Higher Transcendental Functions, Vol. 1. New York: Krieger, pp. 15-20, 1981.

Guillera, J. and Sondow, J. "Double Integrals and Infinite Products for Some Classical Constants Via Analytic Continuations of Lerch's Transcendent." 16 June 2005 http://arxiv.org/abs/math.NT/0506319.  

Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, 2003.

Jeffreys, H. and Jeffreys, B. S. "The Digamma () and Trigamma () Functions." Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 465-466, 1988.

Spanier, J. and Oldham, K. B. "The Digamma Function ." Ch. 44 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 423-434, 1987.