The process of proving that the derivative of the x power of e is equal to the x power of e is as follows:

Derivation is a calculation method in mathematical calculation, which 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.

Extended data:

The method of derivation:

(1) Steps to find the derivative of the function y=f(x) at x0:?

① Find the increment δ y = f (x0+δ x)-f (x0) of the function?

② Find the average change rate?

③ Seek the limit and derivative. ?

(2) 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 loga(x)'=( 1/x)loga(e)？

(3) Four algorithms of derivative:?

①(u v)'=u' v '

②(uv)'=u'v+uv '？

③(u/v)'=(u'v-uv')/ v^2？

④[u(v)]'=[u'(v)]*v' (u(v) is the compound function f[g(x)])?