Answer:
![\dfrac{d(f(x))}{dx} = \dfrac{2}{x}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%28f%28x%29%29%7D%7Bdx%7D%20%3D%20%5Cdfrac%7B2%7D%7Bx%7D)
Step-by-step explanation:
We are given the following function in the question:
![f(x) = \ln (3x^2)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cln%20%283x%5E2%29)
We have to derivate the given function.
Formula:
![\dfrac{d(\ln x)}{dx} = \dfrac{1}{x}\\\\\dfrac{d(x^n)}{dx} = nx^{n-1}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%28%5Cln%20x%29%7D%7Bdx%7D%20%3D%20%5Cdfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%5Cdfrac%7Bd%28x%5En%29%7D%7Bdx%7D%20%3D%20nx%5E%7Bn-1%7D)
The derivation takes place in the following manner
![f(x) = \ln (3x^2)\\\\\dfrac{d(f(x))}{dx} = \displaystyle\frac{d(\ln(3x^2))}{dx}\\\\=\frac{1}{3x^2}\times \frac{d(3x^2)}{dx}\\\\= \frac{1}{3x^2}\times (6x)\\\\=\frac{6x}{3x^2}\\\\=\frac{2}{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cln%20%283x%5E2%29%5C%5C%5C%5C%5Cdfrac%7Bd%28f%28x%29%29%7D%7Bdx%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7Bd%28%5Cln%283x%5E2%29%29%7D%7Bdx%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B3x%5E2%7D%5Ctimes%20%5Cfrac%7Bd%283x%5E2%29%7D%7Bdx%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B1%7D%7B3x%5E2%7D%5Ctimes%20%286x%29%5C%5C%5C%5C%3D%5Cfrac%7B6x%7D%7B3x%5E2%7D%5C%5C%5C%5C%3D%5Cfrac%7B2%7D%7Bx%7D)
![\dfrac{d(f(x))}{dx} = \dfrac{2}{x}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%28f%28x%29%29%7D%7Bdx%7D%20%3D%20%5Cdfrac%7B2%7D%7Bx%7D)
2.41667, you can also find a converter online.
So if you have 192 marbles and you want to group them in groups of 15 marbles each
you would see how many times 15's there are in 192 or how many 192's would go into 15
so 192/15 or
12 and 12/15
406 and 411 because there is at least 400 sheets because of the 4 boxes of 100 so there would have to be more than 400 because of the loose sheets
The answer is 2.09 I hope this helped you