The primitive function of (f '(LNX)) / 3x

The primitive function of (f '(LNX)) / 3x

∫(f'(lnx))/(3x) dx
= (1/3)∫d f(lnx)
=(1/3)f(lnx) + C
The primitive function of (f '(LNX)) / 3x = (1 / 3) f (LNX) + C

We know that a and B are constants, and a ≠ 0, f (x) = - ax + B + axlnx, f (E) = 2 (E = 2.71828 (1) find the value of real number B; (2) find the monotone interval of function f (x)

(1) From F (E) = 2, we can get - AE + B + aelne = b = 2, so the value of real number B is 2; (2) from (1), we can get f (x) = - ax + 2 + axlnx, so f ′ (x) = - A + alnx + ax · 1x = alnx, because a ≠ 0, so when a > 0, we can get x > 1 from F ′ (x) > 0, we can get 0 < x < 1 from F ′ (x) < 0; when a < 0, we can get 0 < x < 1 from F ′ (x) > 0, we can get x > 1 from F ′ (x) < 0 The results show that: when a > 0, the monotone increasing interval of function f (x) is (1, + ∞), and the monotone decreasing interval is (0, 1); when a < 0, the monotone increasing interval of function f (x) is (0, 1), and the monotone decreasing interval is (1, + ∞),;

The function f (x) = (x ^ 2 + ax + a) e ^ (- x) (a is a constant, e is the base of natural logarithm). X belongs to R
(1) Determine the value of a so that the minimum value of F (x) is 0
(2) It is proved that if and only if a = 5, the maximum of F (x) is 5
(3) This paper discusses the number of real number roots of the equation f (x) + F (x) with respect to X

1. If f '(x) = (2x + a) e ^ (- x) - (x ^ 2 + ax + a) e ^ (- x) = e ^ (- x) (- x ^ 2 + 2x ax) = 0, then x = 0 or x = 2-A, when a = 2, f' (x) = e ^ (- x) (- x ^ 2) ≤ 0, then f (x) decreases monotonically; when a < 2, f '(x) < 0, 2-A > 0, if x < 0, then f' (x) < 0, if 0 < x < 2-A, then f '(x) >

Given the function FX = - a2x2 + LNX (a belongs to R) (1) find the monotone increasing interval of the function FX (2) if the function FX is a decreasing function in the interval (1, + ∞), find the
Given the function FX = - A & # 178; X & # 178; + LNX (a belongs to R) (1) find the monotone increasing interval of the function FX (2) if the function FX is a decreasing function in the interval (1, + ∞), find the value range of the real number a

First of all, the derivative function is one of - 2A x + X, when a is less than or equal to 0, the derivative function is always greater than 0, so it increases in (0, +). When a is greater than 0 (one of 2A under negative root sign, one of 2A under positive root sign), the second question is 1. When a is less than or equal to 0, the derivative function is always greater than 0, so it increases in (0, +), +When a is greater than 0, there is a positive root sign below 2A. If a is less than or equal to 1, then a is greater than or equal to 2. Look at my typing