1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natasha_Volkova [10]
2 years ago
13

Y equals the quotient of the quantity x squared plus 4 times x and the quantity x cubed minus 5.

Mathematics
1 answer:
koban [17]2 years ago
4 0

Given:

Consider the completer question is "Find the derivative \dfrac{dy}{dx} for y=\dfrac{x^2-4x}{x^3-5}."

To find:

The derivative \dfrac{dy}{dx}.

Solution:

Chain rule: \dfrac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)

Quotient rule: \dfrac{d}{dx}\dfrac{f(x)}{g(x)}=\dfrac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}

We have,

y=\dfrac{x^2-4x}{x^3-5}

Differentiate with respect to x.

\dfrac{dy}{dx}=\dfrac{d}{dx}\left(\dfrac{x^2-4x}{x^3-5}\right)

Using chain rule and quotient rule, we get

\dfrac{dy}{dx}=\dfrac{(x^3-5)\dfrac{d}{dx}(x^2-4x)-(x^2-4x)\dfrac{d}{dx}(x^3-5)}{(x^3-5)^2}

\dfrac{dy}{dx}=\dfrac{(x^3-5)(2x-4)-(x^2-4x)(3x^2)}{(x^3-5)^2}

\dfrac{dy}{dx}=\dfrac{2x^4-4x^3-10x+20-3x^4+12x^3}{(x^3-5)^2}

\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}

Therefore, the required answer is \dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}.

You might be interested in
Mark wants to fence 4 rectangular gardens, each with a length of 9 1/4 feet and a width of 4 1/2feet. What is the length of fenc
kolbaska11 [484]

Answer:

110 ft  

Step-by-step explanation:

The length of fencing is four times the perimeter of one garden.

The formula for the perimeter of a rectangle is  

P = 2l + 2w

The total perimeter for all four rectangles is

P = 4× (2l + 2w) = 8l + 8w

Data:

 l = 9¼ ft

w = 4½ ft

Calculation:

P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft

The total length of fencing is 110 ft.

4 0
3 years ago
Blake is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Blake will earn $
Mrac [35]

Answer:

It was played in 3 movies and in 10 commercials.

Step-by-step explanation:

110 times 3 = 330

530 minus 330 = 200

200 divided by 20 = 10

3 0
3 years ago
Create equations to solve for missing angles may be hard for me to solve. Need help on this!!​
Sonja [21]

Answer: A.2x+30=90

wwww

5 0
3 years ago
Each pair of points lies on a line with the given slope. Find x.
Gwar [14]

Answer:

the answer is -2 inorder to get -1 slope

8 0
3 years ago
David, Morris, and Jose are the stars of the schools’ basketball team. In the last game, David earned twice as many points as Mo
Alexus [3.1K]

Answer:

Since he earned one third as many as Jose

it's 8

Step-by-step explanation:

  • \frac{1}{3}  \times 24 = 8
3 0
3 years ago
Other questions:
  • Joanne wants to put wallpaper in her daughter's room. Each wall measure 16.8 feet long by 12.9 feet wide. What is the area of on
    8·1 answer
  • Dan invests £1300 into his bank account.
    15·1 answer
  • the sum of three consecutive even integers is 36. Let X represent the first integer, x + 2 represent the second integer, and x +
    14·1 answer
  • What is the limit in miles per hour if the speed limit is 55 km/hr??
    9·1 answer
  • 11a-8b-9a-3b=
    13·1 answer
  • Plzzz help me with this I’ll give brainliest
    9·1 answer
  • A) Is {a, e,i,o,u} a subset of {a,b,c,d,e,f,g,h,i) <br> Why?<br>​
    9·2 answers
  • True/false: You choose 20 students from the population and calculate the mean of their test scores. You repeat this process 100
    13·1 answer
  • a shirt is marked down 20% off the original price if they're priced it was $24 what is the sale price of the shirt before sales
    7·2 answers
  • What is the slope of (2,-1) and (8,4)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!