Что такое Определение производной?

Definition of Derivative

f'(x) = lim [f(x+Δx) - f(x)] / Δx as Δx→0. Geometric meaning — the slope of the tangent line

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📖1 min read📊Level 6🗺️3 subtopics📅April 16, 2026

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Geometric Meaning of Derivative
f′(x₀) is the tangent of the angle of the tangent line to the graph at point x₀. Tangent equation: y = f(x₀) + f′(x₀)(x - x₀). Normal equation: y = f(x₀) - (x - x₀)/f′(x₀). Application: function approximation
Differential of a Function
The differential dy = f′(x)dx is the linear part of the function's increment. Geometrically: the increment of the ordinate of the tangent. Applications: approximate calculations, error estimation. Example: √101 ≈ 10 + 1/(2·10) = 10.05
Physical Meaning of Derivative
The derivative of distance with respect to time is velocity: v = ds/dt. The derivative of velocity is acceleration: a = dv/dt = d²s/dt². Applications: kinematics, dynamics, electrical engineering (dQ/dt is current)

Определение производной — f'(x) = lim [f(x+Δx) - f(x)] / Δx при Δx→0.

Геометрический смысл — угловой коэффициент касательной..

События развивались под влиянием совокупности факторов.

Развитие определялось действиями участников и обстановкой.

Результаты оказали влияние на дальнейшее развитие событий.

f'(x) = lim [f(x+Δx) - f(x)] / Δx при Δx→0. Геометрический смысл — угловой коэффициент касательной.

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