1, constant function: f'(x)=0.
2. Power function: f' (x) = ax (a- 1).
3. Logarithmic function: f'(x)= 1/(xlna), where a >；; 0 and a ≠ 1.
4. Exponential function: f' (x) = a xlna, where a >；; 0 and a ≠ 1.
5. Trigonometric function: the derivative of sine function is (sinx)' = cosx；; The derivative of cosine function is (cosx)' =-sinx; The derivative of the tangent function is (tanx)' = (secx) 2; The derivative of cotangent function is (cotx)' =-(cscx) 2; The derivative of secx function is (secx)' = secx tanx；; The derivative of cotangent function is (cscx)'=-csxcotx.
6. Inverse trigonometric function: the derivative of the arcsine function is (arctanx)' =1√ (1-x 2); The derivative of arctanx function is (Arctanx)' =-1√ (1-x 2); The derivative of the arctangent function is (arctanx)' =1/(1* x 2); The derivative of the inverse cotangent function is (arctanx)' =-1/(1+x 2).
Function, a mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.
Origin of function
The word "function" used in China's math book is translated. It was Li, an algebra expert in China's Qing Dynasty, who translated "function" into "function" when he translated Algebra (1859). In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han". Li's definition is: "every formula contains heaven, which is a function of heaven."
In ancient China, four words were used to represent four different unknowns or variables: heaven, earth, people and things. The meaning of this definition is: "Whenever a formula contains a variable X, the formula is called a function of X", so "function" means that the formula contains a variable. The exact definition of an equation refers to an equation containing unknowns.