20/35
Simplify it and you will have 4/7
Answer:
C
Step-by-step explanation:
A function cannot have multiple y values for one x value.
Option A lists the y values of -8 and 10 for the x value of -4. Therefore this is not a function.
Option B lists 0, 5, 10, AND 15 all for -1. This can't be a function either.
Option C does not have two of the same x values for different results. Although both 0 and 9 give you the answer of 1 for the y value, this is perfectly okay in a function. This is your answer.
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)
A
Step-by-step explanation:
90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). ...
180 Degree Rotation. When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). ...
270 Degree Rotation.