We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed in [A. Seidenberg, An elimination theory for differential algebra, Univ. of California Publ. in Math. III (2) (1956) 31–66] but no complete solution was given. Our result is a complement to the corresponding result in algebraic geometry, which gives a bound on degrees of polynomial coefficients in effective Nullstellensatz [G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95 (1) (1926) 736–788; E.W. Mayr, A.W. Meyer, The complexity of the word problems for commutative semigroups and polynomial ideals, Adv. Math. 46 (3) (1982) 305–329; W.D. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. 126 (3) (1987) 577–591; J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (4) (1988) 963–975; L. Caniglia, A. Galligo, J. Heintz, Some new effectivity bounds in computational geometry, in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Rome, 1988, in: Lecture Notes in Comput. Sci., vol. 357, Springer, Berlin, 1989, pp. 131–151; N. Fitchas, A. Galligo, Nullstellensatz effectif et conjecture de Serre (théorème de Quillen–Suslin) pour le calcul formel, Math. Nachr. 149 (1990) 231–253; T. Krick, L.M. Pardo, M. Sombra, Sharp estimates for the arithmetic Nullstellensatz, Duke Math. J. 109 (3) (2001) 521–598; Z. Jelonek, On the effective Nullstellensatz, Invent. Math. 162 (1) (2005) 1–17; T. Dubé, A combinatorial proof of the effective Nullstellensatz, J. Symbolic Comput. 15 (3) (1993) 277–296]. This paper is dedicated to the memory of Eugeny Pankratiev, who was the advisor of the first three authors at Moscow State University.