Covid-19 virus has led to a tremendous pandemic in more than 200 countries across the globe, leading to severe impacts on the lives and health of a large number of people globally. The emergence of Omicron (SARS-CoV-2), which is a coronavirus 2 variant, an acute respiratory syndrome which is highly mutated, has again caused social limitations around the world because of infectious and vaccine escape mutations. One of the most significant steps in the fight against covid-19 is to identify those who were infected with the virus as early as possible, to start their treatment and to minimize the risk of transmission. Detection of this disease from radiographic and radiological images is perhaps one of the quickest and most accessible methods of diagnosing patients. In this study, a computer aided system based on deep learning is proposed for rapid diagnosis of COVID-19 from chest x-ray images. First, a dataset of 5380 Chest x-ray images was collected from publicly available datasets. In the first step, the deep features of the images in the dataset are extracted by using the dataset pre-trained convolutional neural network (CNN) model. In the second step, Differential Evolution (DE), Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) algorithms were used for feature selection in order to find the features that are effective for classification of these deep features. Finally, the features obtained in two stages, Decision Tree (DT), Naive Bayes (NB), support vector machine (SVM), k-Nearest Neighbours (k-NN) and Neural Network (NN) classifiers are used for binary, triple and quadruple classification. In order to measure the success of the models objectively, 10 folds cross validation was used. As a result, 1000 features were extracted with the SqueezeNet CNN model. In the binary, triple and quadruple classification process using these features, the SVM method was found to be the best classifier. The classification successes of the SVM model are 96.02%, 86.84% and 79.87%, respectively. The results obtained from the classification process with deep feature extraction were achieved by selecting the features in the proposed method in less time and with less features. While the performance achieved is very good, further analysis is required on a larger set of COVID-19 images to obtain higher estimates of accuracy.