ichidan verb, intransitive verb
smile at someone
Describes the act of directing a smile toward another person. Often implies a gentle, warm, or slightly shy smile.
彼女は私に優しく微笑みかけた。
She smiled gently at me.
赤ちゃんが母親に微笑みかけている。
The baby is smiling at its mother.
Standard kanji spelling.
Variant with 掛ける; less common but still used.
微笑む means simply 'to smile', without necessarily directing it at someone. 微笑みかける explicitly adds the nuance of smiling *at* or *toward* a person.
Compound of 微笑み (noun form of 微笑む 'to smile') + かける (in the sense of directing an action toward someone).