Differentiation and what are the two main operations of calculus?
Fundamental theorem of calculus operation that we would now call integration. The origins of differentiation likewise predate the Fundamental Theorem of Calculus by hundreds of years; for example, in the fourteenth century the notions of "continuity" of functions and "motion" were studied by the Oxford Calculators and other scholars. The historical relevance of the Fundamental Theorem of Calculus is not the ability to calculate these operations, but the realization that the two seemingly distinct operations (calculation of geometric areas, and calculation of velocities) are actually closely related. The first published statement and proof of a rudimentary form of the fundamental theorem, strongly geometric in
Linearity of differentiation Linearity of differentiation In calculus, the derivative of any linear combination of functions equals the same linear combination of the derivatives of the functions; this property is known as linearity of differentiation, the rule of linearity, or the superposition rule for differentiation. It is a fundamental property of the derivative that encapsulates in a single rule two simpler rules of differentiation, the sum rule (the derivative of the sum of two functions is the sum of the derivatives) and the constant factor rule (the derivative of a constant multiple of a function is the same constant multiple of the derivative).