Respiratory rate (RR) serves as an indicator of various medical conditions, such as cardiovascular diseases and sleep disorders. Several studies have employed signal processing and machine learning techniques to extract RR from biosignals, such as photoplethysmogram (PPG). These RR estimation methods were mostly designed for finger-based PPG collected from subjects in stationary situations (e.g., in hospitals). In contrast to finger-based PPG signals, wrist-based PPG are more susceptible to noise, particularly in their low frequency range, which includes respiratory information. Therefore, the existing methods struggle to accurately extract RR when PPG data are collected from wrist area under free-living conditions. The increasing popularity of smartwatches, equipped with various sensors including PPG, has prompted the need for a robust RR estimation method. In this paper, we propose a convolutional neural network-based approach to extract RR from PPG, accelerometer, and gyroscope signals captured via smartwatches. Our method, including a dilated residual inception module and 1D convolutions, extract the temporal information from the signals, enabling RR estimation. Our method is trained and tested using data collected from 36 subjects under free-living conditions for one day using Samsung Gear Sport watches. For evaluation, we compare the proposed method with four state-of-the-art RR estimation methods. The RR estimates are compared with RR references obtained from a chest-band device. The results show that our method outperforms the existing methods with the Mean-Absolute-Error and Root-Mean-Square-Error of 1.85 and 2.34, while the best results obtained by the other methods are 2.41 and 3.29, respectively. Moreover, compared to the other methods, the absolute error distribution of our method was narrow (with the lowest median), indicating a higher level of agreement between the estimated and reference RR values.