Nucleophilic substitution at acyl carbon of a carboxylic acid derivative generally proceeds by addition-elimination mechanism.

Addition-Elimination Mechanism:
This mechanism involves the addition of a nucleophile to the carbonyl group of the carboxylic acid derivative, followed by the elimination of the leaving group. The process can be summarized as follows:

1. Nucleophilic attack: The nucleophile attacks the carbonyl carbon of the carboxylic acid derivative.

2. Tetrahedral intermediate formation: This leads to the formation of a tetrahedral intermediate.

3. Elimination of leaving group: The leaving group is eliminated from the intermediate, resulting in the formation of the desired product.

This mechanism is favored when the carbonyl carbon is sterically unhindered and the leaving group is a good leaving group.

Elimination-Addition Mechanism:
This mechanism involves the elimination of the leaving group from the carboxylic acid derivative, followed by the addition of the nucleophile to the carbonyl group. This process can be summarized as follows:

1. Elimination of leaving group: The leaving group is eliminated from the carboxylic acid derivative.

2. Formation of enolate intermediate: This leads to the formation of an enolate intermediate.

3. Nucleophilic attack: The nucleophile attacks the carbonyl carbon of the enolate intermediate.

4. Protonation: The product is protonated to form the desired product.

This mechanism is favored when the carbonyl carbon is sterically hindered and the leaving group is a poor leaving group.

SN1 Mechanism:
This mechanism involves the formation of a carbocation intermediate, followed by the attack of the nucleophile. This mechanism is not favored in carboxylic acid derivatives because the carbonyl carbon is not a good electrophile.

SN2 Mechanism:
This mechanism involves the simultaneous attack of the nucleophile and the expulsion of the leaving group. This mechanism is not favored in carboxylic acid derivatives because the carbonyl carbon is not a good electrophile.

Thus, the addition-elimination mechanism is the most common mechanism for nucleophilic substitution at the acyl carbon of a carboxylic acid derivative.