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Dementia is a severe cognitive impairment that affects the health of older adults and creates a burden on their families and caretakers. This paper analyzes diverse features extracted from spoken languages and selects the most discriminative features for dementia detection. The paper presents a deep learning-based feature ranking method called dual-net feature ranking (DFR). The proposed DFR utilizes a dual-net architecture, where two networks (called operator and selector) are alternatively and cooperatively trained to simultaneously perform feature selection and dementia detection. The DFR interprets the contribution of individual features to the predictions of the selector network using all of the selector's parameters. The DFR was evaluated on the Cantonese JCCOCC-MoCA Elderly Speech Dataset. Results show that the DFR can significantly reduce feature dimensionality while identifying small feature subsets with comparable or superior performance than the whole feature set. The selected features have been uploaded to https://github.com/kexquan/AD-detection-Feature-selection.