bedingt durch
caused by
Caused, brought about, or influenced by something.
Der Flugausfall war durch das schlechte Wetter bedingt.
The flight cancellation was caused by the bad weather.

conditional / limited
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caused by
Caused, brought about, or influenced by something.
Der Flugausfall war durch das schlechte Wetter bedingt.
The flight cancellation was caused by the bad weather.

'Bedingt' is the past participle of the verb 'bedingen' (to cause, to entail), which means 'verursachen' (to cause) or 'zur Folge haben' (to result in). This origin explains the meaning 'caused by'.
Der Erfolg des Projekts ist durch gute Teamarbeit bedingt.
The success of the project is caused by good teamwork.
When 'bedingt' appears with the preposition 'durch' (by/through), it refers to a cause. When it stands alone or with 'nur' (only), it means 'limited' or 'partial'.
Die gute Ernte war durch das sonnige Wetter bedingt.
The good harvest was caused by the sunny weather.
The expression 'bedingt durch' (caused by) takes the accusative and can either stand directly after the noun it describes or introduce a sentence at the beginning.
Bedingt durch den Feiertag sind die Geschäfte heute geschlossen.
Due to the public holiday, the shops are closed today.
In the meaning 'eingeschränkt' (limited), 'bedingt' is very often combined with the word 'nur' (only). The expression 'nur bedingt' (only to a limited extent) weakens a statement.
Diese Jacke ist nur bedingt für den Winter geeignet.
This jacket is only of limited suitability for winter.
This meaning of 'bedingt' (suspended/conditional) is used almost exclusively in legal contexts. You can recognize it from words such as 'Strafe' (sentence/penalty), 'Haft' (imprisonment), or 'Bewährung' (probation).
Der Angeklagte wurde zu einer bedingten Geldstrafe verurteilt.
The defendant was sentenced to a suspended fine.
partly
'teilweise' and 'bedingt' can both express that something does not apply completely. 'teilweise' simply means: only in part, not completely, or not always. 'bedingt' sounds a bit more formal and often means: only with limitations or only under certain conditions. In many everyday sentences, 'teilweise' is more natural when describing an amount or a state. 'bedingt' fits better when a statement is only true in a limited way or depends on certain conditions.

Nach der Krankheit ist Max nur bedingt belastbar.
After the illness, Max can only handle limited physical or mental strain.
Die Kosten werden teilweise von den Eltern bezahlt.
The costs are partly paid by the parents.