To deduce a noun in mathematics is to deduce a function. Represented by ()'

(1) Find the derivative of the function y=f(x) at x0:

① Find the increment δ y = f (x0+δ x)-f (x0) of the function.

② Find the average change rate.

③ Seek the limit and derivative.

(2) Derivative formulas of several common functions:

①C'=0(C is a constant);

②(x^n)'=nx^(n- 1)

(n∈Q)；

③(sinx)' = cosx；

④(cosx)' =-sinx；

⑤(e^x)'=e^x；

⑥(a^x)'=a^xIna

(ln is the natural logarithm)

(3) Four algorithms of derivative:

①(u v)'=u' v '

②(uv)'=u'v+uv '

③(u/v)'=(u'v-uv')/

Derivative of V 2 (4) Compound Function

The derivative of the compound function to the independent variable is equal to the derivative of the known function to the intermediate variable, multiplied by the derivative of the intermediate variable to the independent variable-called the chain rule.

Extended data:

Derivation is the foundation of calculus and an important pillar of calculus calculation. Some important concepts in physics, geometry, economics and other disciplines can be expressed by derivatives. For example, derivatives can represent the instantaneous speed and acceleration of a moving object, the slope of a curve at a certain point, and the margin and elasticity in economics.

This function will be involved in many economic activities and needs special attention. It is neither an exponential function nor a power function, and its power base and exponent have independent variables X, so it cannot be treated by the differential method of elementary functions. This paper introduces a method to solve this kind of function-logarithmic derivative method.