Derivative, also called derivative function value and WeChat quotient, is an important basic concept in calculus. 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 deduction algorithm is: addition (subtraction) rule: [f (x)+g (x)]' = f (x)'+g (x)'; Multiplication rule: [f (x) * g (x)]' = f (x)' * g (x)+g (x)' * f (x); Division rule: [f (x)/g (x)]' = [f (x)' * g (x)-g (x)' * f (x)]/g (x) 2.
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.