From the same root as *dьrzati + *-nǫti; see *dьrzati for further etymology. Compare also Sanskritधृष्णोति(dhṛṣṇóti, “to dare”) (cognate per Derksen and Trubachev, not necessarily per Vasmer or Chernykh).
Chernykh, P. Ja. (1993) “де́рзкий”, in Историко-этимологический словарь русского языка [Historical-Etymological Dictionary of the Russian Language] (in Russian), 3rd edition, volume 1 (а – пантомима), Moscow: Russian Lang., →ISBN, page 244
Trubachyov, Oleg, editor (1978), “*dьrznǫti”, in Этимологический словарь славянских языков [Etymological dictionary of Slavic languages] (in Russian), numbers 5 (*dělo – *dьržьlь), Moscow: Nauka, page 227
Vasmer, Max (1964–1973) “дерза́ть”, in Oleg Trubachyov, transl., Этимологический словарь русского языка [Etymological Dictionary of the Russian Language] (in Russian), Moscow: Progress