求写一篇关于derivative的英语文章

Derivative
When a function y=f(x) has been defined in (which contains the point ).And ,as d approaches 0 ( ),could be worked out as a certain number,though it could not be exactly the same.This number is called this function‘s derivative at the point ,and could be written as f’( ).
That means f’( ) ( )
And also f’(x) is also a function related to x,so we can call f’(x) is the derived function.
I think we could also say that the derivative is the rate of the change.Just look right as chapter 1 shows.
First we notice as x increases,the value of y also raises up.However,the average increase rate from to ,seem to be much more large than the rate during the same length of time from to .So we could get that though in one certain process of increase,the rate can be variable,can be not uniform.Actually,that the most common phenomenon,different average rates of change of different time may be a more useful number for people.But,if we reduce the length between to ,that we will surely get another number of the rate.As we go on our work to make the smaller and smaller,even approaches 0,we may get the certain number for the change rate at that point,though we could not see the change in such a small interval.In fact that are our eyes cheeting us !y is still increase,and the number of the rate at that corresponding x is what we called the derivative at that point.
As I mentioned before,we have to reduce the to a very very smaller number.The limit is very important as I could show how to solve a maths problem.
For the function of ,how could we solve the derivative when t=2
At first we must know the derivative is the rate of the change.So we could first suppose there is a little interval .And then we try to find the change of the two points.
But we have the precondition is that the is very small ,( ).And then we could consider the output answer as .This is because the is too small that we could ignore it,as we could ignore the .So when the t is 2,the derivative is 10*2+10=30.Otherwise,without the limit,you may not solve the question in this method.
The derivative also could be used in large range of science such as math,physics and even in our daily life.I think the most important role that it could be is a tool to solve function and geometry problems in math.For example,in the chapter 1,we could also use the derivative to represents the slope of the tangent line at a certain x.The same way in reverse,we could solve the slope also.
The step for solving the tangent line:
1.solve f’(x) at for the function y=f(x)
2.use to get the function of the tangent line
Notice,if at point ,the derivative is not defined,but there still has a tangent line,that means the tangent line is perpendicular to the x axis.
If we use the derivative to solve the function problem.For example,if f’(x) is bigger than 0,that means it is a increasing function,on the other hand,the function will be a decreasing one if f’(x) is smaller than zero.When f(x) is 0,the function may has its extreme value at that point.Of course we may then solve the maximum or the minimum value of the function.
Also derivative is very important in physics,also we can say the velocity is the derivative of the displacement,the accleration is the derivative of the velcity,the electric current is the derivative of the electric quantity,and so on.This time,we could use the derivative to solve different questions.Futhermore,in our daily life,we may use the principle of how derivative works in the function to know when we could get the max or the min value we need.