Find the derivative of |x|/(x-1)

1 answer:

4 0

$\bf \cfrac{|x|}{x-1}\iff \cfrac{\sqrt{x^2}}{x-1}\iff \cfrac{(x^2)^{\frac{1}{2}}}{x-1}
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\textit{using the quotient rule}
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\cfrac{dy}{dx}=\cfrac{\frac{1}{2}(x^2)^{-\frac{1}{2}}\cdot 2x(x-1)-(x^2)^{\frac{1}{2}}\cdot 1}{(x-1)^2}$

$\bf \cfrac{dy}{dx}=\cfrac{\frac{x(x-1)-(x^2)^{\frac{1}{2}}}{(x^2)^{\frac{1}{2}}}}{(x-1)^2}\implies \cfrac{dy}{dx}=\cfrac{x(x-1)-(x^2)^{\frac{1}{2}}}{(x^2)^{\frac{1}{2}}(x-1)^2}
\\\\\\\cfrac{dy}{dx}=\cfrac{x(x-1)-|x|}{|x|(x-1)^2}$

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dusya [7]

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A football player is running the length of a 100 yard long football field. For the first part of the field, he runs at a rate of

notka56 [123]

Answer:

$\frac{2}{5}$ th part of the field is covered in the second sprint.

Step-by-step explanation:

A football player is running the length of a 100 yard long football field.

Let player sprints x yards with the speed = 2 yards per second.

So time taken to cover x yards player will take time = $\frac{x}{2}$ seconds

Now rest distance (100 - x) yards when covered with the speed of 4 yards per second, so time taken to cover this distance = $\frac{Distance}{Speed}$

= $\frac{100-x}{4}$ seconds

Now total time taken by the player can be represented by the equation

$\frac{x}{2}+\frac{100-x}{4}=40$

Now we can solve this equation for the value of x.

$\frac{2x+100-x}{4}=40$

x + 100 = 40×4

x + 100 = 160

x = 160 - 100 = 60 yards

And length of the second part will be = 100 - 60 = 40 yards

Now the fraction of the field covered by the player in second sprint will be

= $\frac{40}{100}$

= $\frac{2}{5}$ or 40%

Therefore, $\frac{2}{5}$ th part of the field was covered in second sprint.

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3 years ago

Find the perimeter of the figure to the nearest hundredth. Sorry to ask ANOTHER question on this stuff but I'm doing an assignme

WARRIOR [948]

Answer:

I did my best, but it has been a while. I really hope that this helps

Step-by-step explanation:

so you can find the perimeter of a circle

-----The perimeter of a circle is π × d where d is the diameter so half of that is 1/2 π × d. But If you are going to walk around a semicircle, you need to go halfway around the circle and then across a diagonal to get back to where you started, so the perimeter is 1/2 π × d + d.