Derivation: 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.

Differential: Two sets of numbers A and B are obtained from the function B=f(A). In A, when dx is close to itself, the limit of the function at dx is called the differential of the function at dx, and the central idea of the differential is infinite division.

2. Difference of ratio increment

Derivative: the slope of the function image at a certain point, that is, the ordinate increment (δ y) and the abscissa increment (δ x) are at δ x->; The ratio of 0.

Differential: After the tangent of a function image at a certain point obtains the increment Δ x on the abscissa, the increment obtained on the ordinate is generally expressed as dy.

Calculus, a mathematical concept, is a branch of higher mathematics that studies the differential and integral of functions and related concepts and applications.

Extended data:

The application of differentiation in daily life is to find out the change of a specific index at a certain point in time through nonlinear changes.

For example, the water tank is full, and the relationship between the volume V (liter) of water in the water tank and the time T (second) is V=5-2/(t+ 1).

When t=3, I want to know the water adding rate at this time, so after t=3, I calculate DV/DT = 2/(t+ 1) 2, and when t=3, I get dV/dt= 1/8.

Therefore, it can be concluded that the water in the water tank increases at the rate of 1/8 liters per second within 3 seconds after the start of water injection.

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