2. Introduction to derivation:
Derivation is a calculation method in mathematical calculation, and derivative is defined as the limit of the quotient between the increment of dependent variable and the increment of independent variable when the increment of independent variable tends to zero. When a function has a derivative, it is said to be derivative or differentiable. The differentiable function must be continuous. Discontinuous functions must be non-differentiable.
Some important concepts in physics, geometry, economics and other disciplines can be expressed by derivatives. For example, derivatives can represent the instantaneous speed and acceleration of a moving object, the slope of a curve at a certain point, and the margin and elasticity in economics.
A term in mathematics, that is, the derivative of a function, is expressed by f'(x).
3, college physics with derivative solution:
The derivative in advanced mathematics is also called "WeChat service". Because the molecule dy is differential and the denominator dx is differential, the two are divided (actually related to the limit, but in terms of expression). High school mathematics only learned the geometric meaning of derivatives and some commonly used formulas for derivation, while advanced mathematics (more accurately, calculus or differential calculus) involved deeper and wider.
"D is derivative" means "differential" or "infinitesimal increment". For example, dy represents the differential of y, or represents the tiny increment of y at a certain value (usually considered as infinitesimal). When dealing with some problems, we often encounter the "infinitesimal method", and there will be various quantities expressed by D, such as a certain time infinitesimal for dt, a certain mass infinitesimal for dm and so on.
Some are expressed by second derivative, which you can use by looking at derivative exercises in advanced mathematics.