dripping with sweat; by the sweat of one's brow
Idiomatic expression describing hard physical labor or intense effort, often used adverbially with verbs like 働く (work) or 努力する (strive).
He worked dripping with sweat for his family.
I bought a house with money saved by the sweat of my brow.
Standard spelling using たらして.
Alternate spelling using the kanji 垂らす; less common but still encountered.
From 汗 (sweat) + 水 (water) + 垂らして (dripping), literally 'dripping sweat and water'. The phrase is a fixed idiomatic expression.