Derivative, also called derivative function value. Also known as WeChat quotient, it is an important basic concept in calculus. Derivative is the local property of function. The derivative of a function at a certain point describes the rate of change of the function near that point.
What is a derivative?
The derivative is the "average rate of change" △y/△x ",which is the limit value when △x→0". The derivative value of differentiable function y=f(x) at point (a, b) is f'(a).
Derivative formula of basic elementary function:
The types of functions involved in the derivative formula of basic elementary functions in senior high school mathematics are: constant function, power function, sine function, cosine function, exponential function and logarithmic function.
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.