In astrology, a derivative house describes the affairs of a house when you turn the chart and is used in horary astrology. Chances are that if you're here you're probably trying to figure out how to interpret your horary question.
The houses in horary astrology charts mean the same as in the natal chart. For example, horary questions about boyfriends/girlfriends/husbands/wives have the 7th house as the partner's significator, just like in your birth chart the 7th house relates to how you interact with your partner and long-term marriage/love-related stuff. Again, the meaning of each house is the same whether you're doing horary, natal or electional astrology.
REMINDER OF WHAT EACH HOUSE MEANS
The first house is YOUR house, meaning how you physically look and the ruler of the zodiac sign on the first house is your significator. Ex: Let's say the first house is Capricorn; the ruler is Saturn since Saturn is the traditional ruler of Capricorn.
The second house is the money house NOT job, but money in general.
The third house is communication, short-distance trips and relations with neighbors.
The fourth house is your home life, personal well-being and security, nurturance issues (if any).
The fifth house is casual fun (like casual sex/hookups), creativity, children and what you do in your downtime and your favorite hobbies and activities.
The sixth house are your everyday duties, rituals etc.
The seventh house is about your partnerships in general (not just love-related like boyfriend/girlfriend/marriages, but it is often that).
The eighth house is your sex life, joint finances with your partner, death and occult.
The ninth house is about higher learning (like college/grad school), spirituality, church, long-distance trips, foreign contacts like foreign countries or hot foreign people ;).
The tenth house relates to your career and destiny.
The eleventh house is your hopes and wishes and most importantly YOUR FRIENDSHIPS.
The twelfth house deals with your karmic issues and stuff you keep hidden/secret.
DERIVATIVE HOUSES AKA TURNING THE CHART: I will simplify derivative houses because I know horary and astrology in general is difficult enough. As an example, let's say we ask a question about your husband, he'd be the 7th house since that's the house of partnerships and he's obviously your partner. What we would do is turn the chart so the 7th house now becomes the first house, kind of like your husband is the first house and the person in charge.
The seventh house is now the first house and thus represents your partner's physical self and personality..
The eighth house is now the second house and thus represents partner's money.
The ninth house is now the third house and thus relates to the partner's communication style and short-distance trips and relations with neighbors.
The tenth house is now the fourth house and thus relates to partner's home life and nurturance. i.e. mother in law.
The eleventh house is now the fifth house and thus relates to what the partner does for fun and their dealings with their children and children in general.
The twelfth house is now the sixth house and relates to the partner's daily activities.
In the derivative chart we are now back at the first house which relates back to the seventh house in the horary chart.
The first house is now the seventh house and is therefore how the partner sees you romantically.
The second house is now the eighth house and relates to what the partner shares with you, including sex and money.
The third house is now the ninth house and relates to the partner's long distance travels, ethics, philosophies, faith.
The fourth house is now the tenth house and relates to the partner's career, public status and father figure, boss, landlord.
The fifth house is now the eleventh house and relates to the partner's friends and hopes and wishes.
The sixth house is now the twelfth house and relates to the partner's secrets and karmic issues.
