Differential calculus is the study of the definition, lands, and requisitions of the derivative of a method. The procedure of discovering the derivative is called differentiation. Given a role and a focus in the realm, the derivative at that indicate is a way of encoding the modest-scale conduct of the role close to that indicate. By discovering the derivative of a capacity at each focus in its space, its plausible to handle another role, called the derivative capacity or simply the derivative of the initial role.

In numerical language, the derivative is a straight specialist which inputs a role and yields a second role. This is more conceptual than a significant number of the methodologies concentrated on in primary variable based maths, where roles ordinarily enter a number and yield an additional number. For instance, if the duplicating capacity is given the information several, then it yields six, and if the squaring capacity is given the information several, then it yields nine. The derivative, on the other hand, can take the squaring role as an info. This indicates that the derivative takes every last trace of the qualified information of the squaring method—for example that two is sent to four, three is sent to nine, four is sent to sixteen, et cetera—and utilizes this informative content to handle a different method. (The capacity it transforms manufactures be the copying capacity.)