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:

Linearity of derivative: To find the linear combination of derivative functions is equivalent to finding the derivatives of each part first and then finding the linear combination.

The derivative of the product of two functions is equal to the derivative of one multiplied by the product of the derivative of the other and the derivative of the other.

The derivative function of the quotient of two functions is also a fraction. Where the numerator is the derivative function of the numerator function multiplied by the denominator function minus the derivative function of the denominator function multiplied by the difference of the numerator function, and the denominator is the square of the denominator function.

Derivative formula of basic elementary function:

1 .C'=0(C is a constant);

2 .(Xn)' = nX(n- 1)(n∈Q)；

3 .(sinX)' = cosX；

4 .(cosX)' =-sinX；

5 .(aX)'=aXIna (ln is the natural logarithm)

In particular, (ex)'=ex

6 .(logaX)' =( 1/X)logae = 1/(Xlna)(a & gt； 0, and a ≠ 1)

In particular, (ln x)' =1/x.

7 .(tanX)'= 1/(cosX)2=(secX)2

8 .(cotX)' =- 1/(sinX)2 =-(cscX)2

9 .(secX)'=tanX secX

10.(cscX)'=-cotX cscX

Four algorithms of derivative:

①(u v)'=u' v '

②(uv)'=u'v+uv '

③(u/v)'=(u'v-uv')/ v2

④ Derivative of composite function

[u(v)]'=[u'(v)]*v' (u(v) is a compound function f[g(x)])

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.

Derivative is the foundation of calculus and an important pillar of calculus calculation.