Machine Learning is the study of algorithms that improves the performance at some task with experience.
A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at the tasks improves with the experiences.
Ex: Face Recognition, Document Classification
Deep learning is a subset of machine learning in which data goes through multiple number of non-linear transformations to obtain an output.
Ex: Automated Driving, Leaf Pattern Identification
Data science is much more than machine learning. Data in data science, may or may not come from a machine. Survey data could be manually collected, clinical trials involve a specific type of small data. Also, it might have nothing to do with learning. But the main difference is the fact that data science covers the whole spectrum of data processing, not just the algorithmic or statistical aspects