The derivative

The derivative

Why derivative?It is one of the most important topics in math, both at high school and university.Hence, you will see questions mostly on this topic.It is a highly important topic for the next one, i.e. integration.

What is derivative?There are many definitions and approaches to derivative from all branches of science.So, we may start defining it in many ways. but all of these definitions involve the topic of limit!!

MoreMany real-world phenomena involve changing quantitiesthe speed of a rocket, (physics) the inflation of currency, (economics)the number of bacteria in a culture, (biology)the shock intensity of an earthquake, (seismology)The voltage of an electrical signal (electronics), and so forth.we will develop the concept of a derivative, which is the mathematical tool for studying the rate at which one quantity changes relative to another.

In the future, all will become clear.

The Derivative and the Tangent Line Problem

How can we calculate the slope of the tangent line at the point p of the curve?

What is slop?

Gradient (Slope) of a Straight Line

Secant lines approaching the tangent line at the point P

EXAMPLE 1

Find the slope of the graph of f(x) = 2x 3 at the point (2,1)

The limit process

list the points A, B, C and D in order ofincreasing slope of the tangent line.

Graphs of a function and its derivative

the derivative does not exist

velocity