だす
dasu
Everything だす does is 'out'
The picture Pushing something that was inside out into the open. Only the container changes. だす sends what was inside out; いれる puts what was outside in.
Where the picture shows up in だす
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out of the bag
かばんから財布を出しました。
kaban kara saifu o dashimashita
I took my wallet out of my bag.
Reaching in through the mouth of a bag and drawing the wallet out
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out of your hands
レポートは明日までに出してください。
repōto wa ashita made ni dashite kudasai
Please hand the report in by tomorrow.
The document that was in your hands crossing over to the far side of the desk
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out of your body
電車の中で大きな声を出さないでください。
densha no naka de ōkina koe o dasanai de kudasai
Please don't raise your voice on the train.
A voice that was inside your mouth breaking out into the air of the train
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out into the world
来月、新しい商品を出します。
raigetsu, atarashii shōhin o dashimasu
We're releasing a new product next month.
Goods that were in the warehouse coming out to sit on the display shelf
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it bursts out
急に子どもが泣き出しました。
kyū ni kodomo ga naki dashimashita
The child suddenly burst into tears.
Tears a child was holding in bursting out of their mouth
verb + 出す means it bursts into action; 泣き出す is more abrupt than 泣き始める.
All of it in one picture
だす is the picture of pushing something that was inside out into the open. The wallet comes out of the bag; the report leaves your hands for someone else's; the voice breaks out of your mouth into the carriage; the product comes out of the warehouse into the world; the crying bursts out of a chest that was holding it. Only the container changes — a bag, your hands, your body, a company, a held-back feeling. So 〜だす leaves the feeling of something that was shut in crossing the boundary and showing on the outside.