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
Nezavi [6.7K]
2 years ago
7

Find dy/dx if y =x^3+5x+2/x²-1

Mathematics
1 answer:
stiks02 [169]2 years ago
7 0

<u>Differentiate using the Quotient Rule</u> –

\qquad\pink{\twoheadrightarrow \sf \dfrac{d}{dx} \bigg[\dfrac{f(x)}{g(x)} \bigg]= \dfrac{ g(x)\:\dfrac{d}{dx}\bigg[f(x)\bigg] -f(x)\dfrac{d}{dx}\:\bigg[g(x)\bigg]}{g(x)^2}}\\

According to the given question, we have –

  • f(x) = x^3+5x+2
  • g(x) = x^2-1

Let's solve it!

\qquad\green{\twoheadrightarrow \bf \dfrac{d}{dx}\bigg[ \dfrac{x^3+5x+2 }{x^2-1}\bigg]} \\

\qquad\twoheadrightarrow \sf \dfrac{(x^2-1) \dfrac{d}{dx}(x^3+5x+2) - ( x^3+5x+2)  \dfrac{d}{dx}(x^2-1)}{(x^2-1)^2 }\\

\qquad\twoheadrightarrow \sf \dfrac{(x^2-1)(3x^2+5)  -  ( x^3+5x+2) 2x}{(x^2-1)^2 }\\

\qquad\pink{\sf \because \dfrac{d}{dx} x^n = nx^{n-1} }\\

\qquad\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-(2x^4+10x^2+4x)}{(x^2-1)^2 }\\

\qquad\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-2x^4-10x^2-4x}{(x^2-1)^2 }\\

\qquad\green{\twoheadrightarrow \bf \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}\\

\qquad\pink{\therefore  \bf{\green{\underline{\underline{\dfrac{d}{dx} \dfrac{x^3+5x+2 }{x^2-1}}  =  \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}}}}\\\\

You might be interested in
Mariana wants to research a career in veterinary medicine. Where could she find accurate and objective information?
Amiraneli [1.4K]

Answer

Step-by-step explanation:

6 0
3 years ago
Please helppppp it’s due soon and I’m already failing my class!!!
Margarita [4]

Answer:

For an equation like:

y = a*x + b

a is the slope, and this is the rate of change of the function.

For the case of the problem, we know that the equation represents the amount of oxygen in the spaceship as a function of time. Where as the time passes, the quantity of oxygen decreases.

Then the slope is the rate of change that tells how the quantity of oxygen changes as time passes. Then the slope is the amount of oxygen that is consumed per unit of time.

8 0
3 years ago
Insert grouping symbols to make each number sentence true 7*8-6+3=17
NNADVOKAT [17]

Answer:

7*(8-6)+3

Step-by-step explanation:

Grouping symbols are parentheses; trial and error can lead you to this answer.

Checking, we must use order of operations (PEMDAS). First, we evaluate what's inside parentheses.

7 * 2 + 3

Then multiply:

14 + 3

Then add

17

7 0
3 years ago
I need help ASAP thank you
PIT_PIT [208]

Answer:

E

Step-by-step explanation:

every single graph is asimethrical because they have no trend.

4 0
3 years ago
100 points anwser asap
natita [175]

Answer:

23

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • How can x^2=x^2+2x+9 be set up as a system of equations
    12·1 answer
  • Bruno is sewing a large rectangular tablecloth for a restaurant. He has 30 square feet of fabric, and the length of the table cl
    12·1 answer
  • PLEASE HELP! What is the value of x? Enter your answer in the box. x =
    14·1 answer
  • Find the volume of a right circular cone that has a height of 6.7 in and a base with a circumference of 9.8 in. Round your answe
    13·1 answer
  • How Did You Do? Rate Your On a Scale Of1 to 5, with 5 as the highest score. then Write a brief evaluation of your work. Note wha
    11·2 answers
  • if a recipe for cookies calls for 3/4 of a cup of sugar, and you want to quadruple the recipe, how many cups of sugar will you n
    8·2 answers
  • Convert units to complete each equation. 61/2 ft = ___ in?
    14·2 answers
  • What number is a solution of the inequality 3&lt;3x-15
    8·2 answers
  • I Need Help Finding The Answer To m
    5·1 answer
  • I’ve spent too long on this. Pls help!!
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!