Derivatives
(อัตราอนุพันธ์)
Definition
Derivatives (อัตราอนุพันธ์) Hard Skill
Derivatives are mathematical tools used to measure the rate at which a function changes with respect to a variable, essential in understanding dynamic systems and solving problems in calculus and applied sciences.
Expertise Level
Level 1
Basic
1. Understands the concept of a derivative as an instantaneous rate of change.
2. Can calculate basic derivatives of simple functions using standard rules.
3. Recognizes common derivative formulas such as power and constant rules.
Level 2
Intermediate
1. Applies derivative rules like product, quotient, and chain rule to more complex functions.
2. Interprets the meaning of derivatives in applied contexts such as velocity and slope.
3. Solves problems involving higher-order derivatives and implicit differentiation.
Level 3
Advanced
1. Utilizes derivatives in advanced applications such as optimization and differential equations.
2. Analyzes functions in multi-variable calculus including partial derivatives.
3. Integrates derivatives within mathematical modeling to solve real-world problems.
