Beth42, A large percentage of the Derry City Cemetery in Northern Ireland has now been transcribed and is available online at :-
https://www.derrystrabane.com/cemeteryrecordsI have done a search and your Elizabeth MITCHELL (nee SNELL) is situated at Grave Number F-b-108 in the City Cemetery. She shares the grave with 4 other people.
Deceased Parents Place of Birth Place of Residence Age Date of Death Date of Burial Grave Location Cemetery Proprietor Residence of Proprietor Notes Reference #
James Mitchell James & Elizabeth Mitchell Orchard Place, Foyle Road Orchard Place 4 years 5 months 28 May 1875 31 May 1875 F-b-108 Derry City Cemetery James Mitchell Orchard Place, Foyle Road CRS00620
Elizabeth Mitchell William & Elizabeth Snell Magilligan Orchard Row 41 years 02 Jul 1876 04 Jul 1876 F-b-108 Derry City Cemetery James Mitchell Orchard Row CRS001088
William Mitchell Joseph & Rebeca Mitchell Galliagh Wapping Lane 54 years 26 Jan 1877 28 Jan 1877 F-b-108 Derry City Cemetery James Mitchell 17 Orchard Place CRS001266
George Mitchell James & Jane Mitchell Foyle Road Foyle Road 1 years 6 months 14 Aug 1886 16 Aug 1886 F-b-108 Derry City Cemetery James Mitchell Foyle Road late Orchard Street CRS005153
Anne Mitchell John & Annie Doak Derry Wapping Lane 58 years 05 Dec 1886 07 Dec 1886 F-b-108 Derry City Cemetery James Mitchell Foyle Road CRS005266
I hope this is helpful to you.
Good luck
BobDenn.