What is the derivative formula? What are the specific examples of the derivative formula under the 11th-grade Mathematics curriculum in Vietnam? Under the new program, what are the required outcomes regarding derivatives for 11th-grade students in Vietnam?

View Post in Vietnamese: >> Công thức đạo hàm là gì? Cho ví dụ cụ thể về công thức đạo hàm lớp 11? Học sinh lớp 11 cần đạt những yêu cầu nào về đạo hàm theo chương trình mới?

What is the derivative formula? What are the specific examples of the derivative formula under the 11th-grade Mathematics curriculum in Vietnam?

11th-grade students may refer to the following information on the derivative formula and specific examples of the derivative formula under the 11th-grade Mathematics curriculum:

What is the derivative formula? What are the specific examples of the derivative formula under the 11th-grade Mathematics curriculum in Vietnam?

The derivative is an important concept in mathematics, especially in Calculus. It represents the rate of change of a function at a specific point on the graph of that function. In other words, the derivative indicates whether the function is increasing, decreasing, or constant at a certain point.

Geometric meaning: The derivative at a point is the slope of the tangent line to the graph of the function at that point.

*Example:

The graph of the function is increasing: Derivative is positive.

The graph of the function is decreasing: Derivative is negative.

The graph of the function reaches an extreme point (maximum or minimum): Derivative equals 0.

*Basic derivative formulas for 11th grade

Below are some basic derivative formulas that you often encounter in the 11th-grade Mathematics program:

*Derivative of basic functions:

Constant function: (c)' = 0 (where c is a constant)

Power function: (x^n)' = n*x^(n-1)

Exponential function: (a^x)' = a^x * ln(a)

Logarithmic function: (log_a(x))' = 1 / (x*ln(a))

*Trigonometric functions:

(sin(x))' = cos(x)

(cos(x))' = -sin(x)

(tan(x))' = 1/cos^2(x)

(cot(x))' = -1/sin^2(x)

*Derivative calculation rules:

Derivative of sum, difference: (u ± v)' = u' ± v'

Derivative of product: (u*v)' = u'v + uv'

Derivative of quotient: (u/v)' = (u'v - uv') / v^2 (with v ≠ 0)

Derivative of composite function: If y = f(u) and u = g(x) then y' = f'(u)*u'

Specific example

Problem: Calculate the derivative of the function y = 2x^3 + 5x - 1

Solution:

Apply the derivative formula of sum, difference, and power functions, we have:

y' = (2x^3)' + (5x)' - (1)'

y' = 23x^(3-1) + 5*1 - 0

y' = 6x^2 + 5

Thus, the derivative of the function y = 2x^3 + 5x - 1 is y' = 6x^2 + 5.

Problem: Calculate the derivative of the function y = sin(2x)

Solution:

This is an example of a composite function. Set u = 2x, then y = sin(u).

Apply the derivative formula of composite functions and the derivative of the sine function, we have:

y' = cos(u)*u'

y' = cos(2x)*2

y' = 2*cos(2x)

Thus, the derivative of the function y = sin(2x) is y' = 2*cos(2x).

*Note: Information is for reference only./.

What is the derivative formula? Provide specific examples of the derivative formula for 11th grade? What requirements should 11th-grade students meet according to the new program?

Under the new program, what are the required outcomes regarding derivatives for 11th-grade students in Vietnam?

Under subsection 3, Section 5 of the General Education Program in Mathematics issued under Circular 32/2018/TT-BG/DDT, the required outcomes regarding derivatives for 11th-grade students in Vietnam include:

Content	Required outcomes
Concept of derivative. Geometric meaning of the derivative	- Recognize some problems leading to the concept of a derivative such as: determining the instantaneous velocity of an unevenly moving object, determining the rate of temperature change. - Recognize the definition of a derivative. Be able to calculate the derivative of some simple functions by definition. - Recognize the geometric meaning of the derivative. - Establish the equation of the tangent line of the function graph at a point on the graph. - Recognize the number e through problems modeling bank interest rates.
Rules for calculating derivatives	- Be able to calculate the derivative of some basic elementary functions (such as polynomial functions, simple radical functions, trigonometric functions, exponential functions, logarithmic functions). - Be able to use formulas for calculating the derivative of the sum, difference, product, quotient of functions and derivative of composite functions. - Solve some problems related to other subjects or practical issues associated with derivatives (e.g., determining the instantaneous velocity of an unevenly moving object,...).
Second derivative	- Recognize the concept of the second derivative of a function. - Be able to calculate the second derivative of some simple functions. - Solve some problems related to other subjects or practical issues associated with the second derivative (e.g., determining acceleration from the velocity-time graph of an uneven motion,...).

What are the objectives of the 11th-grade Mathematics curriculum in Vietnam regarding basic mathematical knowledge and skills?

Under the General Education Program in Mathematics issued under Circular 32/2018/TT-BGDĐT, specific regulations are as follows:

Mathematics at the lower secondary level aims to help students achieve the following main objectives:

+ Contribute to the formation and development of mathematical competence with the requirement to: pose and answer questions during reasoning, solve problems, perform reasonable reasoning when solving problems, and prove not-too-complex mathematical propositions;

+ Be able to use mathematical models (mathematical formulas, algebraic equations, representations,...) to describe situations in some uncomplicated real-life problems; use mathematical language combined with ordinary language to express mathematical content as well as demonstrate evidence, reasoning, and results; present ideas and how to use tools and means for learning mathematics to perform a learning task or to describe arguments or proofs in mathematics.

+ Have basic mathematical knowledge and skills about:

++ Numbers and Algebra: The number system (from natural numbers to real numbers); calculation and use of calculation tools; algebraic language and symbols; transform algebraic expressions, equations, systems of equations, inequalities; use function language to describe (model) some processes and phenomena in reality.

++ Geometry and Measurement: Geometry and Measurement content at this education level include Visual Geometry and Plane Geometry.

Visual Geometry continues to provide language, symbols, and descriptions (at a visual level) of real-world objects (plane shapes, solid shapes); establish some common geometric models; calculate some geometric elements; develop spatial imagination; solve some simple practical problems related to Geometry and Measurement.

Plane Geometry provides knowledge and skills (at a reasoned logic level) about geometric relationships and some common plane figures (points, lines, rays, line segments, angles, two parallel lines, triangles, quadrilaterals, and circles).

++ Statistics and Probability: Collect, classify, represent, analyze, and process statistical data; analyze statistical data through frequency, and relative frequency; recognize some simple statistical laws in practice; use statistics to understand the basic concepts of the experimental probability of an event and the probability of an event; recognize the meaning of probability in practice.

+ Help students have an initial understanding of careers related to mathematics; have a sense of career orientation based on abilities, interests, conditions, and personal circumstances; and orient streamlining after lower secondary education (continue studying, vocational training, or engage in working life).

>> CLICK HERE TO READ THIS ARTICLE IN VIETNAMESE

What are the 03+ 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025? What are the eligibility requirements for providing internal extra classes for 11th-grade Mathematics in Vietnam?

What are the newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025? What are the bases for assessing the training results of 11th-grade students in Vietnam?

What is the formula for the tangent line equation? What are the objectives regarding basic arithmetic and algebra skills of the 11th-grade Mathematics curriculum in Vietnam?

What is the formula for calculating the volume of a pyramid? What is the grade at which students in Vietnam will learn to calculate the volume of a pyramid?

What is the arithmetic sequence formula? What is the grade whose Mathematics curriculum covers arithmetic sequence in Vietnam?

What are the 05 1st mid-semester question papers for 11th-grade Mathematics for review? What are the objectives of the 11th-grade Mathematics curriculum in Vietnam?

Vietnam: What are the Top 3 1st end-of-semester question papers and answers for 11th-grade Mathematics? What are the perspectives on developing the 11th-grade Mathematics curriculum?

What are power reducing formula in Vietnam? When do students in Vietnam learn power reducing formula?

What is the Logarithm formula? When do students in Vietnam learn about Logarithm formula?

- This translation is generated by OpenAI's GPT-4o model;

- Lawnet's response to our user's question is provided above. If you need further information, please send an email to hotrophaply@lawnet.vn;

- This article is for reference only;

- The regulations referred to in this article might have been annulled by the time you read it;

- For inquiries about the copyright of this article, please send an email to banquyen@lawnet.com;

Địa chỉ:	19 Nguyễn Gia Thiều, P. Võ Thị Sáu, Q.3, TP. Hồ Chí Minh
Điện thoại:	(028) 3930 3279 (06 lines)
E-mail:	info@lawnet.vn