C'=0(c is a constant)

(x a)' = ax (a- 1), where a is a constant and a≠0.

(a^x)'=a^xlna

(e^x)'=e^x

(logax)'= 1/(xlna), a>0 and a ≠ 1

(lnx)'= 1/x

(sinx)'=cosx

(cosx)'=-sinx

(tanx)'=(secx)^2

(secx)'=secxtanx

(cotx)'=-(cscx)^2

(cscx)'=-csxcotx

(arcsinx)'= 1/√( 1-x^2)

(arccosx)'=- 1/√( 1-x^2)

(arctanx)'= 1/( 1+x^2)

(arccotx)'=- 1/( 1+x^2)

(shx)'=chx

(chx)'=shx

d(cu)=cdud(u+-v)=du+-dvd(uv)=vdu+udvd(u/v)=(vdu-udv)/v^2

The derivative is

Important basic concepts in calculus. When the independent variable x of the function y=f(x) generates an increment δ x at the point x0, if there is a limit a in the ratio of the increment δ y of the function output value to the increment δ x of the independent variable when δ x tends to 0, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx.

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.

For differentiable function f(x), x? F'(x) is also a function called the derivative function of f(x). The process of finding the derivative of a known function at a certain point or its derivative function is called derivative. Derivative is essentially a process of finding the limit, and the four algorithms of derivative also come from the four algorithms of limit. Conversely, the known derivative function can also reverse the original function, that is, indefinite integral. The basic theorem of calculus shows that finding the original function is equivalent to integral. Derivation and integration are a pair of reciprocal operations, both of which are the most basic concepts in calculus.