Ask the known derivative formula: y = C "C is a constant" its derivative function y '= 0, find the derivative function of y = 2x!

Ask the known derivative formula: y = C "C is a constant" its derivative function y '= 0, find the derivative function of y = 2x!

y'=2'*x+2*x'
=0*x+2*1
=2

1. If a ＞ B, C ＜ D, can we judge which is bigger and which is smaller between a + C and B + D
② If a ＞ B, C ＜ D, can we judge which is bigger and which is smaller between a-2c and b-2d
③ If a ＞ B, C ＜ D, can we deduce AC ＞ BD
④ If a ＞ B, C ＜ D, and C ≠ 0, D ≠ 0, can I quit a / C ＞ B / D
2. Verification
① If a > b, C < D, then A-D > b-c
② If a > b, AB > 0, then 1 / a < 1 / b
③ If a > b > 0, C < d < 0, then AC < BD

1 (1) if a = 5, B = 2, C = 8, d = 9, then a + C > b + D if a = 5, B = 2, C = 8, d = 12, then a + CB, CB, - C > - D, at the same time, - 2C > - 2D, so when the unequal signs are in the same direction, the addition of the two sides is still in the same direction, we can get that a-2c > b-2d (3) can not be determined, because we do not know whether the four numbers are positive or negative

In △ ABC, a, B and C are the three inner angles respectively, and a, B and C are the opposite sides of the three inner angles respectively. The root sign 2 (sin ＾ 2 a-SiN ＾ 2 c) = (a-b) SINB is known twice, and the radius of the circumscribed circle of △ ABC is root sign 2
(1) Find the degree of angle C
(2) Find the maximum value of △ ABC area s

(1) According to the sine theorem, Sina = A / (2R), sinc = C / (2R), SINB = B / (2R), where R is the radius of the circumscribed circle of a triangle,
SO 2 radical 2 [a ^ 2 / (4R ^ 2) - C ^ 2 / (4R ^ 2)] = (a-b) B / (2R)
SO 2 radical 2 (a ^ 2-C ^ 2) = 2 radical 2 (a-b) B
So a ^ 2 + B ^ 2-C ^ 2 = AB, from the cosine theorem we get COSC = (a ^ 2 + B ^ 2-C ^ 2) / 2Ab = AB / (2Ab) = 1 / 2
So C = 60 degrees
(2) According to the sine theorem, C = 2 * radical 2 * sinc = radical 6, so a ^ 2 + B ^ 2-AB = C ^ 2 = 6
Because a ^ 2 + B ^ 2-AB > = 2Ab AB, so ab