1, y=c(c is a constant) y'=0.

2、y=x^n y'=nx^(n- 1)

3、y=a^x y'=a^xlna,y=e^x y'=e^x

4、y=logax y'=logae/x，y=lnx y'= 1/x

5、y=sinx y'=cosx

6、y=cosx y'=-sinx

7、y=tanx y'= 1/cos^2x

8、y=cotx y'=- 1/sin^2x

Derivation rule of 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 Derivation: Finding 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.