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

2, y = x μ, y' = μ x (μ- 1) (μ is constant, μ≠0).

3、y=a^x,y'=a^x lna； y=e^x,y'=e^x。

4、y=logax，y ' = 1/(xlna)(a & gt； 0 and a ≠1); y=lnx，y'= 1/x .

5、y=sinx，y’= cosx .

6、y=cosx，y'=-sinx .

7、y=tanx,y'=(secx)^2= 1/(cosx)^2。

8、y=cotx,y'=-(cscx)^2=- 1/(sinx)^2。

9、y=arcsinx,y'= 1/√( 1-x^2)。

10、y=arccosx,y'=- 1/√( 1-x^2)。

1 1、y=arctanx,y'= 1/( 1+x^2)。

12、y=arccotx,y'=- 1/( 1+x^2)。

13、y=shx，y’= CHX .

14、y=chx，y'=sh x .

15、y=thx,y'= 1/(chx)^2。

16、y=arshx,y'= 1/√( 1+x^2)。

Characteristics of derivative products:

1, monotonicity:

(1) If the derivative is greater than zero, it will increase monotonically; If the derivative is less than zero, it decreases monotonically; The derivative equal to zero is the stagnation point of the function, not necessarily the extreme point. To judge monotonicity, the derivatives of the left and right values of the entry point are required.

(2) If the known function is increasing function, the derivative is greater than or equal to zero; If the known function is a subtraction function, the derivative is less than or equal to zero.

2, concave and convex:

The concavity and convexity of differentiable function is related to the monotonicity of its derivative. If the derivative function of a function increases monotonically in a certain interval, then the function in this interval is concave downward, otherwise it is convex upward.

If the second derivative function exists, it can also be judged by its positive and negative. If it is always greater than zero in a certain interval, the function is concave downward in this interval and convex upward in this interval. The concave-convex boundary point of a curve is called the inflection point of the curve.

Reference to the above content: Baidu Encyclopedia-Derivation