Find the value of x

Derivative of<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3x%7D%5E%7B2%7D%20-%202x%20-%201%20%7D%7B%20%7Bx%7D%5E%7B2

Anastaziya [24]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

Step-by-step explanation:

we would like to figure out the derivative of the following:

$\displaystyle \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

to do so, let,

$\displaystyle y = \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

By simplifying we acquire:

$\displaystyle y = 3 - \frac{2}{x} - \frac{1}{ {x}^{2} }$

use law of exponent which yields:

$\displaystyle y = 3 - 2 {x}^{ - 1} - { {x}^{ - 2} }$

take derivative in both sides:

$\displaystyle \frac{dy}{dx} = \frac{d}{dx} (3 - 2 {x}^{ - 1} - { {x}^{ - 2} } )$

use sum derivation rule which yields:

$\rm\displaystyle \frac{dy}{dx} = \frac{d}{dx} 3 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

By constant derivation we acquire:

$\rm\displaystyle \frac{dy}{dx} = 0 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

use exponent rule of derivation which yields:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ - 1 -1} ) - ( - 2 {x}^{ - 2 - 1} )$

simplify exponent:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ -2} ) - ( - 2 {x}^{ - 3} )$

two negatives make positive so,

$\displaystyle \frac{dy}{dx} = 2 {x}^{ -2} + 2 {x}^{ - 3}$

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

$\displaystyle \frac{dy}{dx} = \frac{2 }{x^2}+ \frac{2}{x^3}$

simplify addition:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

and we are done!

5 0

3 years ago

Mathematics pls solve i need to check my answers bcs my teacher is sucky

Lilit [14]

If H is the circumcenter, then each of EH, FH, and GH are perpendicular bisectors of the legs BC, CD, and DB, respectively. So, for instance, EH cuts BC in half so that BE and EC have the same length.

Also, BH, CH, and DH are radii to the circumcircle of the triangle, so they all have the same length.

(1) CD = CF + FD = 2 • FD = 2 • 32 = 64

(2) CE = BE = 26

(3) HD = HC = 33

(4) GD = 1/2 • BD = 1/2 • 58 = 29

(5) By the Pythagorean theorem,

HG² + GD² = HD²

so

HG = √(33² - 29²) = 2 √(62)

(6) Similar to (5); by the Pythagorean theorem,

HF² + FD² = HD²

so

HF = √(33² - 32²) = √(65)

5 0

3 years ago

Maria has a bag with 6 red marbles, 6 blue marbles, and 4 green marbles looking Maria picks one . She does not replace it and sh

Sati [7]

Answer: Hello there!

initially Maria has 6 red marbles, 6 blue marbles, and 4 green marbles.

You know that in the first pick, Maria gets a green marble ( this means that now there are 3 green marbles left)

Now we want to know the probability that she gets a red marble on the second pick.

Now there are 6 + 6 + 3 = 15 marbles in the bag, and 6 of them are red ones. Then the probability of getting one red is the number of red ones divided by the total amount ( which is the ratio of red marbles to total marbles)

this is 6/15.

now you can see that there is no 6/15 in the options, so we need to see which one is equivalent.

if we took the option C, 2/5, and multiply both denominator and numerator by 3, we get (3*2)/(3*5) = 6/15, then 2/5 and 6/15 are equivalents.

Then the correct answer is C.

Step-by-step explanation:

5 0

3 years ago

Find the value of x. Round to the nearest degree.

Sever21 [200]

If you draw a line from the X to the opposite side you get 5 and the long side is the hypotenuse
So this is sine opposite over hypotenuse
Sin ^-1= 5/14
Answer 20.9 degrees

5 0

3 years ago

Howard works 7 hours each day. He earns $8.00 per hour. Which number sentence shows the total amount of money he earns in one da

Stells [14]

7x8=56
He works 7 hours a day, so for each hour Howard earns 8$. 7hoursx8$ per hour=56$ for 7 hours

6 0

3 years ago