Derivative is defined as the limit of the quotient between the increment of dependent variable and the increment of independent variable when the increment of independent variable tends to zero. When a function has a derivative, it is said to be derivative or differentiable. The differentiable function must be continuous. Discontinuous functions must be non-differentiable.

The definition method should be to use limit to get derivative, and the method is to use derivative formula directly.

Derivative formulas of several common functions;

① C'=0(C is a constant);

②(x^n)'=nx^(n- 1)(n∈q)；

③(sinx)' = cosx；

④(cosx)' =-sinx；

⑤(e^x)'=e^x；

⑥ (a x)' = a A Xin (ln is natural logarithm).

⑦ (Inx)'= 1/x(ln is natural logarithm)

(3) Four algorithms of derivative:

①(u v)'=u' v '

②(uv)'=u'v+uv '

③(u/v)'=(u'v-uv')/ v^2