Derailer used as chain tensioner for peddle chain.

It looks like you need a degree to pilot that thing lol! Looks fun!
Shifting with trigger shifters you must keep in mind on the 4 levers [Top Down] [Bottom Ups]. Meaning the levers on the Top of the shifters make you go Down. The levers on the Bottom of the shifters make you go Up.

If you also notice on both my shifters is the colors Red, Yellow, Green. So this is how it works:

Red chainring 1
Red sprockets (1,2,3)

Yellow chainring 2
Yellow sprockets (3,4,5)

Green chainring 3
Green sprockets (5,6,7)

Chainring transition sprockets (3,5)

This gives you 9 sequential non redundant gear ratios.

With gears when under a strong load it's easy to go from large to small but harder to go from small to large. So here's an old mountian bike trick.

If a path or road doesn't have any really sharp curves and/or stops, momentum can carry you over rolling hills. With sprockets in order to go lower you have to go small to large (hard to do while under a load). With chainrings in order to go lower you have to go large to small (easy to do while under a load).

I'll use a 3x7 as an example. To contend with rolling hills you'd use only rear sprocket (4) and only shift the front chainrings.

At the top of the hill be in 3(4) gather as much speed as possible going down the hill. Once you begin to climb the next hill and begin to feel a load increase drop into 2(4). If the load becomes to hard before topping the hill you can drop into 1(4). As you top the hill shift back to 3(4) to start the sequence again. With this trick you can keep a fairly high momentum going through rolling hills.
 
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