A Level 9709: Differentiation | 现代数学启蒙

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Topic: Differentiation

Definition of Differentiation

Differentiation is a mathematical process that calculates the rate at which a function changes. It is used to find the derivative of a function, which represents the slope or rate of change of the function at any given point.

The derivative of a function f(x) is denoted as f'(x) or dy/dx. It measures how the function f(x) changes as x changes. The derivative gives us information about the steepness of the curve, the direction of the curve (increasing or decreasing), and the rate at which the function is changing.

To find the derivative of a function, we apply differentiation rules and formulas. These rules allow us to find the derivative of various types of functions, including polynomials, exponential functions, logarithmic functions, and trigonometric functions.

The derivative is an important concept in calculus as it has applications in various fields such as physics, economics, engineering, and computer science. It helps us analyze and understand the behavior of functions, optimize functions, and solve problems involving rates of change.

Remember that differentiation is the process of finding the derivative of a function, and the derivative represents the rate of change of the function.

Example:

Find the derivative of the function

Answer:

The derivative of f(x) is given by:

f'(x) = 6x - 4

Exercises:

Find the derivative of the function

Answers for the exercises above:

Other Resources:

Textbook: "Calculus Made Easy" by Silvanus P. Thompson

Online tutorial: Khan Academy - "Introduction to Derivatives"

Video

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