(1) 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^xLna

(3) Four algorithms of derivative:

①(u v)'=u' v '

②(uv)'=u'v+uv '

③(u/v)'=(u'v-uv')/ v^2

(4) Derivative of composite function

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 an important pillar of calculus!

Derivative formula and its proof

The following will list the derivatives of several basic functions and their derivation processes:

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

2.y=x^n y'=nx^(n- 1)

3.y=a^x y'=a^xlna

y=e^x y'=e^x

4.y=logax y'=logae/x

y=lnx y'= 1/x

5.y=sinx y'=cosx

6.y=cosx y'=-sinx

7.y = Tanks Y' =1/cos 2x

8.y=cotx y'=- 1/sin^2x

9 . y = arcsinx y'= 1/√ 1-x^2

10 . y = arc cosx y'=- 1/√ 1-x^2

1 1 . y = arctanx y'= 1/ 1+x^2

12 . y = arccotx y'=- 1/ 1+x^2

I don't know if this is what you want, but I can only offer so much.