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n200080 [17]
3 years ago
8

Find dy / dx for ex + y = y.

Mathematics
1 answer:
asambeis [7]3 years ago
5 0

Answer:  The required value of \dfrac{dy}{dx} is \dfrac{y}{1-y}.

Step-by-step explanation:   We are given to find the value of \dfrac{dy}{dx} from the following equation :

e^{x+y}=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Taking natural logarithm on both sides of equation (i), we have

\ln e^{x+y}=\ln y\\\\\Rightarrow x+y=\ln y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

Differentiating both sides of equation (ii) with respect to x, we get

\dfrac{d}{dx}(x+y)=\dfrac{d}{dx}\ln y\\\\\\\Rightarrow 1+\dfrac{dy}{dx}=\dfrac{1}{y}\dfrac{dy}{dx}\\\\\\\Rightarrow \left(\dfrac{1}{y}-1\right)\dfrac{dy}{dx}=1\\\\\\\Rightarrow \dfrac{1-y}{y}\dfrac{dy}{dx}=1\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{y}{1-y}.

Thus, the required value of \dfrac{dy}{dx} is \dfrac{y}{1-y}.

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3 years ago
Use the net to compute the surface area of the three-dimensional figure.
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9514 1404 393

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  382 square units

Step-by-step explanation:

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__

<em>Additional comment</em>

You can reject the first two answer choices immediately, because they are odd. Each face will have an area that is the product of integers, so will be an integer. There are two faces of each size, so <em>the total area of this figure must be an even number</em>.

You may recognize that the dimensions are 8, 8+1, 8-1. Then the area is roughly that of a cube with dimensions of 8: 6×8² = 384. If you use these values (8, 8+1, 8-1) in the area formula, you find the area is actually 384-2 = 382. That area formula is A = 2(LW +H(L+W)).

3 0
3 years ago
Free points !!!!!<br><br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B1%7D%20" id="TexFormula1" title=" \sqrt[3]{1} " a
Artist 52 [7]

Answer:

hello there

your answer is <u>1</u>

Step-by-step explanation:

hope it helps....

thanks for the free points!!!

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2 years ago
I’ve been stuck on this question for an hour? I need help ASAP! Thanks! What is the total surface area of the trapezoidal prism?
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3 years ago
Hiii please help i’ll give brainliest if you give a correct answer tysm!
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Answer:

d 380

Step-by-step explanation:

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