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3 years ago

X 1.4.17

Mathematics

1 answer:

AlekseyPX3 years ago

4 0

Answer:

WQDQW

Step-by-step explanation:

WQDW

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Find gradient xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to x, assuming y = y(x).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for dy/dx :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If y ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

4 0

3 years ago

Mr. Shaw need 27 markers. He can buy them in pack of 10 markers or as single markers. What are all the different ways. Mr. Shaw

Aleks [24]

Times by 10 then add 7

3 0

3 years ago

Jacob and 6 of his friends went out to eat. They decided to split the bill evenly. Each person paid $14.93. What was the total b

jasenka [17]

Answer:

$104.51

Step-by-step explanation:

No.of people = 7

How much each person paid = $14.93

How much is the total bill = $14.93 x 7

= $104.51

I was bored so I added the steps lol

8 0

3 years ago

Read 2 more answers

How many x intercepts appear on the graph of this polynomial function? f(x)=x^4-5x^2 1 x intercept 2 x intercepts 3 x intercepts

Bumek [7]

You can find the number of x intercepts by setting f(x) equal to zero giving you 0=x^4-5x^2. You can factor out an x^2 and divide on both sides (when you divide 0 by anything it is still zero so the x^2 disappears), and you are left with 0=x^2-5, which you can solve easily giving you x=+/- sqrt(5). However, the original equation also has an x intercept at (0,0) which you can see by plugging 0 in for x. So the grand total of x intercepts is 3!

5 0

3 years ago

Read 2 more answers

1 4/7 _______ - 15/ 21

Sati [7]

Answer: -11/5

Step-by-step explanation:

$\frac{11}{7}$ ÷ $\frac{-15}{21}$