Out of curiosity, I tried searching familysearch for offspring of Joseph and Ann using a variant spelling heginbotham which featured on the peripheries of my family research. My formula, once I'd got past the initial very basic search page, was:
First names left blank
Surname heginbotham
Event Birth
Place Derbyshire
Year say 1793 +/- 10 (thus allowing bit of leeway on the possible date of marriage. It could also be worth trying say 1803 +/- 20)
Relationship Parents
Father, first names Joseph
Father, surname left blank
Mother, first names Ann
Mother, surname left blank
The first few entries in the results seemed to me to be way off target, but you might find something in those listed further down under the 'less strong matches', eg a Matthew Heginbotham bp Great Longstone 14 Sep 1794, father Joseph. And, on further inspection, other entries in this list - eg for a Bettey Higgenbothom - look highly intriguing...
Good luck
Birtle