The geometric meaning of derivative is the slope of the tangent of the curve.

Its physical meaning is instantaneous speed, etc.

Mathematical definition:

Derivative is an important basic concept in calculus. The limit of the quotient between the increment of the dependent variable and the increment of the independent variable when the increment of the independent variable tends to zero. When a function has a derivative, it is said to be derivative or differentiable. The differentiable function must be continuous. Discontinuous functions must be non-differentiable. Derivative is essentially a process of finding the limit, and the four algorithms of derivative come from the four algorithms of limit.

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