Detailed steps for finding the derivative y of the following function equal to Cos

Detailed steps for finding the derivative y of the following function equal to Cos

y=cos（3x^2-π/6)
y'=-sin（3x^2-π/6) * 3*2x=-6xsin（3x^2-π/6)
Y = cos (3x Square-6)
Y '= - sin (3x-6) * (3x-6)'
=-6xsin (3x Square-6)
If the least common multiple of two numbers is & nbsp; 252 and the greatest common divisor is & nbsp; 7, and the greater of the two numbers is not a multiple of a decimal, then the two numbers are______ .
252 = 2 × 2 × 3 × 3 × 7, the greatest common factor of two numbers is & nbsp; 7, 7 is their only common prime factor, then 2 and 3 are their unique prime factors, 2 × 2 × 7 = 28, 3 × 3 × 7 = 63; so the answers are: 28 and 63
Finding the derivative of function y = SIN3 (5x)
Three is a cube
I don't know
3sin^2 (5x)*cos(5x)*5
=15sin^2(5x)*cos(5x)
15 * cos(5x) * sin^2(5x)
15sin2(5x)cos(5x)
The greatest common factor of the two numbers is 15, the least common multiple is 180, and the large number is not a multiple of the decimal, the two numbers are______ .
Because 180 △ 15 = 12, the unique product of prime factors of two numbers is 12, 12 = 1 × 12 = 3 × 4, and because large numbers are not multiples of decimals, they can not be 1 and 12. These two numbers can only be: 15 × 3 = 45, 15 × 4 = 60; so the answer is: 45 and 60
Given the function f (x) = x ^ 3 + LNX + 2, then the inequality f [x (x-1)]
The function is monotone increasing function, so the solution of the original inequality is inequality x (x-1)
If the least common multiple of two natural numbers is 84 and the greatest common factor is 14, and the large number is not a multiple of a decimal, then the two numbers are () and ()
28 and 52
Least common multiple / greatest common factor
=84/14
=6
So the product of two numbers minus the common part is 6
So it's 2 * 3 or 1 * 6
2 * 14 3 * 14 or 1 * 14 6 * 14
=28 32 14 84
It's not a decimal multiple. So 14 84 is rounded off
32
Given the function f (x) = lnx-a (x-1) / X (a ∈ R) (1) find the monotone interval of F (x) (2) prove the inequality 1 / lnx-1 / X-1
(1) Function f (x) = LNX - [a (x-1) / x], domain x (0, + ∞);
F '(x) = (1 / x) - (A / X & # 178;), Let f' (x) = 0, we get the function stagnation point equation: (1 / x) - (A / X & # 178;) = 0, the solution is x = a;
1、 If A0, then 0
If the greatest common factor of two numbers is 7, the least common multiple is 252, and the greater of the two numbers is not a multiple of a decimal, then the two numbers are?
The product of two numbers is: 252 × 7 = 1764 = 2 × 2 × 3 × 3 × 7 × 7
If the greatest common factor of two numbers is 7, then both numbers have a factor of 7
If a large number is not a multiple of a decimal, then in addition to the factor 7,
One contains only factor 2, and the other contains only factor 3
These two numbers:
7×2×2=28
7×3×3=63
7 126
7 and 126
252 / 7 = 36 = 2 * 2 * 3 * 3 (4 * 9 without multiple relation)
therefore
28 63
Given the function f (x) = 12x2 + LNX. (1) find the monotone interval of function f (x); (2) prove: when x > 1, 12x2 + LNX < 23x3
(1) We know that the domain of definition of function is {x | x ＞ 0}, ∵ f ′ (x) = x + 1X, ∵ f ′ (x) ＞ 0, ∵ f (x) monotone increasing interval is (0, + ∞). (2) it is proved that let g (x) = 23x3-12x2-lnx, ∵ g ′ (x) = 2x2-x-1x, ∵ when x ＞ 1, G ′ (x) = (x − 1) (2x2 + X + 1) x ＞ 0, ∵ g (x) be increasing function on (1, + ∞), ∵ g (x) ＞ G (1) = 16 ＞ 0, ∵ When x > 1, 12x2 + LNX < 23x3
There are two numbers, one of which has 10 divisors and the other has 11 divisors. The least common multiple of the two numbers is 2800. What are the two numbers? (= 3=
These two numbers are 400 and 280
112 = 2 * 2 * 2 * 2 * 7 has 10 divisors: 1, 2, 4, 8, 16, 7, 14, 28, 56, 112 350 = 2 * 5 * 5 * 7 has 11 divisors: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 350
There is no answer to this question