Answer:
A
Step-by-step explanation:
We have the equation:
![x^2+xy-3y=3](https://tex.z-dn.net/?f=x%5E2%2Bxy-3y%3D3)
Take the derivative of both sides with respect to x:
![\frac{d}{dx}[x^2+xy-3y]=\frac{d}{dx}[3]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E2%2Bxy-3y%5D%3D%5Cfrac%7Bd%7D%7Bdx%7D%5B3%5D)
Implicitly differentiate:
![2x+y+x\frac{dy}{dx}-3\frac{dy}{dx}=0](https://tex.z-dn.net/?f=2x%2By%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D-3%5Cfrac%7Bdy%7D%7Bdx%7D%3D0)
Solve for dy/dx:
![\frac{dy}{dx}(x-3)=-2x-y\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%28x-3%29%3D-2x-y%5C%5C)
Divide:
![\frac{dy}{dx}=-\frac{2x+y}{x-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B2x%2By%7D%7Bx-3%7D)
To find dy/dx at (2, 1), substitute 2 for x and 1 for y. So:
![\frac{dy}{dx}_{(2, 1)}=-\frac{2(2)+1}{2-3}=-\frac{5}{-1}=5](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D_%7B%282%2C%201%29%7D%3D-%5Cfrac%7B2%282%29%2B1%7D%7B2-3%7D%3D-%5Cfrac%7B5%7D%7B-1%7D%3D5)
Hence, our answer is A.
Answer: They are similar in that when you multiply 2 fractions, you merely multiply the numerators together and the denominators together they are different in that a division still remains once the multiplication is completed.
Step-by-step explanation: ^
Answer:
the one on the right y=4x
Step-by-step explanation:
even if u switch out x it will yeah