That question is not easily answered. Calculus, as it is taught to undergraduates, is not really a developing branch of mathematics. However, calculus has many broader definitions, and many of those are very much in development. By the very fact that you are posting this question, I am not certain you have the exposure to enough terminology that would allow me to answer this question. Many developing fields utilize calculus (as it is taught to undergraduates). Frequently, though, the mathematics in those fields is not under development, but rather development occurs with the applications of the mathematics (finding additional uses for the theorems).
If you were to try to classify Calculus, it has roots in at least three of the major mathematical disciplines (algebra, analysis, and topology). Algebraically, one can define a calculus over a set where many of the operations are similar (but not equivalent to) the operations of differentiation and integration. In analysis, calculus is extended to any field possessing a complete metric, and modern approaches are extremely varied (typically some form of measure theory at their core). Point-set topology is fairly well understood, but "calculus" led to the study of differential geometry, differential manifolds, and more. In each of these disciplines, an accomplished mathematician would see the roots of their studies in undergraduate calculus, but to a student without the necessary training, these disciplines may appear to be completely foreign, even if that student completed and excelled at all undergraduate calculus classes.