Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If the derivative of a function exists at a certain point, it is said to be derivative at this point, otherwise it is called non-derivative. However, the differentiable function must be continuous; Discontinuous functions must be non-differentiable.
For differentiable function f(x), x? F'(x) is also a function called the derivative function of f(x). The process of finding the derivative of a known function at a certain point or its derivative function is called 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 mother square (i.e. Formula ③).
4. If there is a compound function, use the chain rule to deduce it.