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Derby were the more attacking of the two sides from the start, Jamie Ward sending a shot just wide inside the opening 10 minutes.
The Rams continued to look the more likely to score of the two sides, until Chris Cohen found the back of the net for the visitors in the 31st minute, forcing a Sharp cross into the goal with his second attempt.
The hosts had a chance for an equaliser through an unusual source, as right-back John Brayford broke into the box to have a shot that was just wide of the post.
Conor Sammon and Ward teamed up on the edge of the Forest box just before half time, the latter sending a curling effort just wide in the final attacking play of the half.