After deriving a curve, is the slope of the tangent passing through a certain point equal to the derivative?

After deriving a curve, is the slope of the tangent passing through a certain point equal to the derivative?

We should pay attention to which derivative, generally speaking

On the slope of derivative
Let me give you an example to ask the tangent equation of y = root x at point a (1,1) The derivative of the equation is the slope of the tangent equation

The definition of derivative is that in a given neighborhood, when the independent variable x has the variable △ x at x0, the corresponding function has the variable △ y, and the two variables are divided. When △ x tends to 0, the limit of the ratio of the two variables exists. The essence of the slope is Y / x, and the essence of the two variables is the same

Why is the slope derivative?

Slope = LIM (△ X - > 0) [△ Y / △ x] = dy / DX

How to calculate 25X (120-360 △ 4)

25X(120-360÷4)=25x120x(1-3/4)=25x120x1/4=25x30=750

Simple calculation of 7.35 △ 7.35 × 0.25

Remove bracket 1 △ 0.25 = 4

Simple calculation of 8.7 + 1.2 × 0.35

8.7×1.2×0.5×0.7=8.7+0.6×0.7=8.7+0.42=9.12

Calculate with recursive equation!
0.78+8.4÷4.2×3.6 10.33÷（0.46-0.36）×3.4 （9.6-1.69÷1.3）×40
4.1+（10.1-0.9）÷2

First of all, we should pay attention to the operation order of addition, subtraction, multiplication and division. Multiplication and division should be calculated first, and then addition and subtraction. If there are brackets in the formula, the part in the brackets should be calculated first. In the brackets, we should also pay attention to multiplication and division first, addition and subtraction then calculation. The detailed process is as follows: 0.78 + 8.4 △ 4.2 × 3.6 = 0.78 + 2x3.6 = 0.78 + 7.2 = 7.9810.33 ^

The progress of recursive equation calculation
How to multiply 56 by 32 is a simple method

56x32
=56x(30+2)
=56x30+56x2
=1680+112
=1792

The following is a recursive calculation
15*27-3000/25        2.216+64*42/28         3.（3244-282）*12/26=            

15*27-3000/25
＝405－120
＝285
216+64*42/28
＝216＋2688÷28
＝216＋96
＝120
（3244-282）*12/26
＝2962×12÷26
＝35544÷26
＝17772/13

100 trace recursive equation calculation