na-adjective
graceful; willowy; soft and tender
Describes a person, especially a woman, or a movement that is elegantly slender, supple, and gentle. Often used in literary or poetic contexts.
彼女のたおやかな立ち居振る舞いに見とれた。
I was captivated by her graceful bearing.
風に揺れる柳の枝はたおやかだ。
The willow branches swaying in the wind are willowy and soft.
優雅 is a more common word for 'elegant' or 'graceful' and can describe a wider range of refined things, while たおやか specifically emphasizes a slender, supple, and tender gracefulness, often with a literary feel.
しなやか means 'supple' or 'flexible' and can refer to both physical flexibility and mental resilience. たおやか focuses more on a delicate, graceful softness and is less about resilience.
The exact derivation is uncertain. The word is native Japanese, and the kanji 嫋 is used for its meaning of 'slender' and 'graceful', but the historical origin of the reading たおやか is unclear.