1. Understand some practical background of the concept of derivative (such as instantaneous velocity, acceleration, slope of tangent of smooth curve, etc.). ); Master the definition of the derivative of a function at a point and the geometric meaning of the derivative; Understand the concept of derivative function.

2. Memorize the basic derivative formula; Master the derivation rules of sum, difference, product and quotient of two functions. Knowing the derivation rules of composite functions will lead to the derivation of some simple functions.

3. Understand the relationship between monotonicity of differentiable function and its derivative; Understand the necessary and sufficient conditions for the derivative function to obtain the extreme value at a certain point (the sign of the derivative is different on both sides of the extreme value point); Will solve some practical problems (general reference 1). Note: In the above formula, a n represents the n power of A. The maximum and minimum values of unimodal function.

2. Geometric series: a (n+ 1)/an = q, where n is a natural number. (2) General formula: an = a1* q (n-1); Generalization: an = am q (n-m); (3) summation formula: sn = n * a1(q =1) sn = a1(1-q n)/(1-q) = (a1) (1-q) * q n (that is, a-AQ n) (premise: q is not equal to 1) (4) properties: ① if m, n, p, q∈N and m+n = p+q, then am an = AP. ② In geometric series, the sum of every k term still becomes geometric series in turn. (5) "G is the equal median of A and B" and "G 2 = AB (G ≠ 0)". (6) In geometric series, the first term A 1 and the common ratio q are not zero.