I suppose it depends on how you define "everyday life", but in digital image processing, derivatives can be used as a relatively simple method for edge detection.
For example, the Sobel and Prewitt operators (1st derivative) and the Laplacian operator (2nd derivative) can be used as filter kernels to detect edges in images.
For example, the Sobel and Prewitt operators (1st derivative) and the Laplacian operator (2nd derivative) can be used as filter kernels to detect edges in images.