1, the derivative is closely related to physics, geometry and algebra: tangent can be found in geometry; Instantaneous rate of change can be found in algebra; Speed and acceleration can be found in physics.

2. Derivative, also known as epoch number and WeChat quotient (the concept in differentiation), is a mathematical concept abstracted from the problems of speed change and tangent of curve (the direction of vector speed), also known as change rate.

3. Some important concepts in physics, geometry, economics and other disciplines can be expressed by derivatives. For example, derivatives can represent the instantaneous velocity and acceleration of a moving object (in terms of linear motion, the first derivative of displacement versus time is instantaneous velocity and the second derivative is acceleration), the slope of a curve at a point, the margin and elasticity in economics.

Extended data:

The derivative function of a function composed of the sum, difference, product, quotient or mutual combination of basic functions can be derived from the derivative rule of the function. The basic deduction rules are as follows:

1, Linearity of Derivation: Finding the linear combination of derivative functions is equivalent to finding the derivatives of each part first and then finding the linear combination.

2. Derivative function of the product of two functions: one derivative times two+one derivative times two.

3. The derivative function of the quotient of two functions is also a fraction: (derivative times mother-derivative times mother) divided by mother square.

4. If there is a compound function, use the chain rule to deduce it.

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