Answer: The required derivative is 
Step-by-step explanation:
Since we have given that
![y=\ln[x(2x+3)^2]](https://tex.z-dn.net/?f=y%3D%5Cln%5Bx%282x%2B3%29%5E2%5D)
Differentiating log function w.r.t. x, we get that
![\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [x'(2x+3)^2+(2x+3)^2'x]\\\\\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [(2x+3)^2+2x(2x+3)]\\\\\dfrac{dy}{dx}=\dfrac{4x^2+9+12x+4x^2+6x}{x(2x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{8x^2+18x+9}{x(2x+3)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5Bx%27%282x%2B3%29%5E2%2B%282x%2B3%29%5E2%27x%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5B%282x%2B3%29%5E2%2B2x%282x%2B3%29%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B4x%5E2%2B9%2B12x%2B4x%5E2%2B6x%7D%7Bx%282x%2B3%29%5E2%7D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B8x%5E2%2B18x%2B9%7D%7Bx%282x%2B3%29%5E2%7D)
Hence, the required derivative is
L = 6 a^2 b, W = 3 a b
The area of a rectangle:
A = L x W =
= 6 a² b · 3 a b = 18 a³ b²
Answer:
The probability is 1/28,561
Step-by-step explanation:
Here, we want to find the probability that each of the players will receive exactly one ace.
In a deck of cards, we have 4 suites of 13 cards each, with each of the suites consisting of 1 ace.
So, the probability of getting an ace for each of the four players will be 4/52 = 1/13
Now, the probability of each of the players getting exactly one ace will be; first got one ace , second got one , third got one and fourth got one.
mathematically, this probability will be 1/13 * 1/13 * 1/13 * 1/13 = (1/13)^4 = 1/28,561
Answer:
D is not a function.
Step-by-step explanation:
The first option is a function because it makes up a straight line. The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function. The third option is also a function because there is no more than one point for each x value. The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.
Answer:
c = -20
Step-by-step explanation:
-21=1/2c-11
-21+11=1/2c
-10=1/2c
-10*2=c
-20=c
