The derivative function of a known function can be calculated by using the limit of change rate according to the definition of derivative. In practical calculation, most common analytic functions can be regarded as the result of sum, difference, product, quotient or mutual compound of some simple functions.

As long as the derivative functions of these simple functions are known, the derivative functions of more complex functions can be calculated according to the derivative law.

Extended data:

Derivation rule of derivative

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 derivative: the linear combination of derivative function is equivalent to finding the derivative of each part first, and then finding the linear combination (i.e. Formula ①).

2. Derivative function of the product of two functions: one derivative times two+one derivative times two (i.e. Formula ②).

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

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

References:

Derivation-Baidu Encyclopedia