In calculus even more than other areas, the Wolfram Language packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced by new methods being discovered at Wolfram Research, the algorithms in the Wolfram Language probably now reach almost every integral and differential equation for which a closed form can be found.
Dt — total derivatives
CoordinateChartData — computations in curvilinear coordinates
Limit — directed and undirected limits, univariate and multivariate
DSolve — symbolic solutions to differential equations
Derivative — symbolic and numerical derivative functions
DifferentialRoot — general representation of linear differential solutions