Bài 1: Cho hàm số y = (m-1)x + 2 (1)

A) Findi

Romashka [77]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}$

Part B)

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

Step-by-step explanation:

We have the equation:

$\displaystyle x^2y+y^2x=6$

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 x:

$\displaystyle \frac{d}{dx}\Big[x^2y+y^2x\Big]=\frac{d}{dx}\big[6\big]$

The derivative of a constant is 0. We can expand the left:

$\displaystyle \frac{d}{dx}\Big[x^2y\Big]+\frac{d}{dx}\Big[y^2x\Big]=0$

Differentiate using the product rule:

$\displaystyle \Big(\frac{d}{dx}\big[x^2\big]y+x^2\frac{d}{dx}\big[y\big]\Big)+\Big(\frac{d}{dx}\big[y^2\big]x+y^2\frac{d}{dx}\big[x\big]\Big)=0$

Implicitly differentiate:

$\displaystyle (2xy+x^2\frac{dy}{dx})+(2y\frac{dy}{dx}x+y^2)=0$

Rearrange:

$\displaystyle \Big(x^2\frac{dy}{dx}+2xy\frac{dy}{dx}\Big)+(2xy+y^2)=0$

Isolate the dy/dx:

$\displaystyle \frac{dy}{dx}(x^2+2xy)=-(2xy+y^2)$

Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}$

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:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{2(2)(1)+(1)^2}{(2)^2+2(2)(1)}$

Evaluate:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{4+1}{4+4}=-\frac{5}{8}$

Then by the point-slope form:

$y-y_1=m(x-x_1)$

Yields:

$\displaystyle y-1=-\frac{5}{8}(x-2)$

Distribute:

$\displaystyle y-1=-\frac{5}{8}x+\frac{5}{4}$

Hence, our equation is:

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

5 0

2 years ago

Together, Emily and Charlotte have a total of 60 strawberries. Emily sats 4 times the amount that Charlotte eats. How many straw

ehidna [41]

Answer:

12

Step-by-step explanation:

Since Emily eats four times the amount that Charlotte eats, then Emily will eat: = (4 × x) = 4x. Therefore, Charlotte eats 12 strawberries

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One half of a number p is at least 100

4vir4ik [10]

so then P could be any number greater then or equal to 200,hope this helps,please vote me brainliest

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3 years ago

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What is the surface area means

PIT_PIT [208]

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.

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Make A the subject of the formula r= <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Ba%7D%7B3%7D%20%7D%20

DaniilM [7]

Answer:

Huh

Step-by-step explanation:

<h2>3-4=8+7-87+2Kknnjajajaaa</h2>

THANGINA MO TANONG MO SA PAGONG VOVO MO VOVO TALAGA 1V1 ML

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