The instantaneous change rate of derivative is solved Which of you really understands derivative? High school derivative is just a simple concept, sometimes confusing. How can the instantaneous rate of change be determined, especially the derivative of X should be an approximate value, The derivative is a specific value. For example, when y = x ^ 2 + 2x is the derivative of x = 2, another point of the function image must be known. The value should be an ideal value by using the derivative formula. Because the derivative is the rate of change, all must be within the range of change, and here is to reduce the range of change to the minimum to get a specific value of a variable

The instantaneous change rate of derivative is solved Which of you really understands derivative? High school derivative is just a simple concept, sometimes confusing. How can the instantaneous rate of change be determined, especially the derivative of X should be an approximate value, The derivative is a specific value. For example, when y = x ^ 2 + 2x is the derivative of x = 2, another point of the function image must be known. The value should be an ideal value by using the derivative formula. Because the derivative is the rate of change, all must be within the range of change, and here is to reduce the range of change to the minimum to get a specific value of a variable

It is said that this is the thought of limit in University. If we narrow the scope infinitely and the infinity approaches zero, we can probably see it as an instant, like the speed of a certain instant of variable speed motion

Why is the instantaneous rate of change called derivative?

Derivative is an important basic concept in calculus. When the increment of the independent variable approaches zero, the limit of the quotient between the increment of the dependent variable and the increment of the independent variable. When a function has a derivative, it is said that the function is differentiable or differentiable. The differentiable function must be continuous. The discontinuous function must not be differentiable. Derivative is essentially a process of finding the limit, The four arithmetic of derivative comes from the four arithmetic of limit

Definition of rate of change and derivative
Given the function (y = x ^ 2 + 1) ^ 1 / 2, find the average change rate of the function on [x, x + △ x]
Finding the derivative of a function at x = 1

The average rate of change can be expressed by {f (x2) - f (x1)} / (x2-x1), which is called the average rate of change of F (x) from X1 to x2