Answer:
Part A)

Part B)

Step-by-step explanation:
We have the equation:

Part A)
We want to find the derivative of our function, dy/dx.
So, we will take the derivative of both sides with respect to <em>x:</em>
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The derivative of a constant is 0. We can expand the left:
![\displaystyle \frac{d}{dx}\Big[x^2y\Big]+\frac{d}{dx}\Big[y^2x\Big]=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5CBig%5Bx%5E2y%5CBig%5D%2B%5Cfrac%7Bd%7D%7Bdx%7D%5CBig%5By%5E2x%5CBig%5D%3D0)
Differentiate using the product rule:
![\displaystyle \Big(\frac{d}{dx}\big[x^2\big]y+x^2\frac{d}{dx}\big[y\big]\Big)+\Big(\frac{d}{dx}\big[y^2\big]x+y^2\frac{d}{dx}\big[x\big]\Big)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBig%28%5Cfrac%7Bd%7D%7Bdx%7D%5Cbig%5Bx%5E2%5Cbig%5Dy%2Bx%5E2%5Cfrac%7Bd%7D%7Bdx%7D%5Cbig%5By%5Cbig%5D%5CBig%29%2B%5CBig%28%5Cfrac%7Bd%7D%7Bdx%7D%5Cbig%5By%5E2%5Cbig%5Dx%2By%5E2%5Cfrac%7Bd%7D%7Bdx%7D%5Cbig%5Bx%5Cbig%5D%5CBig%29%3D0)
Implicitly differentiate:

Rearrange:

Isolate the dy/dx:

Hence, our derivative is:

Part B)
We want to find the equation of the tangent line at (2, 1).
So, let's find the slope of the tangent line using the derivative. Substitute:

Evaluate:

Then by the point-slope form:

Yields:

Distribute:

Hence, our equation is:

I’m gonna assume it’s 5x(2)+45x
10x+45x=55x
So since each car wash equals $7, you round 12 to 10 and $7 * 10 = $70.
Plus, 22 to 20.
So, $70 * 20 = $1400
So the answer is 1,400
Respuesta:
19
Explicación paso a paso:
Si se van a plantar 361 limoneros en un campo cuadrado;
Entonces, el número de plantas en cada fila debe ser el mismo por columna;
Sea el número de plantas por hilera = x
Número total de plantas = x²
361 = x²
Saca la raíz cuadrada de ambos lados
√361 = √x²
19 = x
Número de plantas por hilera = 19
Answer:
10
Step-by-step explanation:
bh/2
b=5
h=4
=5×4/2
=20/2
=10