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
givi [52]
3 years ago
10

3√x -2/x^2please show step by step of differentiation before combining the terms. ​

Mathematics
1 answer:
EastWind [94]3 years ago
3 0

Answer:

Step-by-step explanation:

Before we differentiate, let us assign a variable to the function. Let y be equal to the function i.e let y = 3√x -2/x²

In differentiation if y = ax^{n}, then \frac{dy}{dx} = nax^{n-1} where n is a constant and dy/dx means we are differentiating the function y with respect to x.

Applying the formula o the question given;

y= 3\sqrt{x}  -2/x^2\\y = 3{x}^\frac{1}{2}  - 2x^{-2} \\\\

On differentiating the resulting function;

\frac{dy}{dx} = \frac{1}{2}*3x^{\frac{1}{2}-1 }   - (-2)x^{-2-1} \\\\\frac{dy}{dx} = \frac{1}{2}*3x^{-\frac{1}{2}} + 2x^{-3}\\ \\\frac{dy}{dx} = \frac{1}{2}*{\frac{3}{x^{\frac{1}{2} } }} + \frac{2}{x^{3} } \\\\\frac{dy}{dx} = {\frac{3}{2x^{\frac{1}{2} } }} + \frac{2}{x^{3} }\\\\\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }

To combine the terms, we will add up by finding their LCM.

\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }\\\frac{dy}{dx}  = \frac{3x^3+4\sqrt{x} }{2x^{3} \sqrt{x}}

You might be interested in
Prove the following statement.
jolli1 [7]
<h2>Step-by-step explanation:</h2>

As per the question,

Let a be any positive integer and b = 4.

According to Euclid division lemma , a = 4q + r

where 0 ≤ r < b.

Thus,

r = 0, 1, 2, 3

Since, a is an odd integer, and

The only valid value of r = 1 and 3

So a = 4q + 1 or 4q + 3

<u>Case 1 :-</u> When a = 4q + 1

On squaring both sides, we get

a² = (4q + 1)²

   = 16q² + 8q + 1

   = 8(2q² + q) + 1

   = 8m + 1 , where m = 2q² + q

<u>Case 2 :-</u> when a = 4q + 3

On squaring both sides, we get

a² = (4q + 3)²

   = 16q² + 24q + 9

   = 8 (2q² + 3q + 1) + 1

   = 8m +1, where m = 2q² + 3q +1

Now,

<u>We can see that at every odd values of r, square of a is in the form of 8m +1.</u>

Also we know, a = 4q +1 and 4q +3 are not divisible by 2 means these all numbers are odd numbers.

Hence , it is clear that square of an odd positive is in form of 8m +1

3 0
3 years ago
Someone help me asap?
laila [671]
4) 8n
5) x=27
6) 2n=22
7)5
6 0
3 years ago
HELP? I don't understand at all!!​
ivanzaharov [21]
I do not know at all I am sorry
8 0
3 years ago
NO LINKS I NEED REAL ANSWERS <br> what are the 2 missing numbers on the blanks?
zavuch27 [327]

Answer:

Step-by-step explanation:

P1 = (2000, 1000)  in the form (x1,y1)

P2 = (2012, 3400) in the form (x2,y2)

m = (y2-y1 / x2-x1)

m = ( 3400-1000 ) / (2012 - 2000)

m = 2400 / 12

m = 200

y = 200x + 800

8 0
3 years ago
A population of 1,750 cheetahs decreases by 10% per year. How many cheetahs will there be in the population after 11 years? Roun
Triss [41]

Answer:

The answer is C. 546.

If a population decreases by 11%, that means that 89% (100% - 11% = 89%) of cheetahs remains each number. 89% can be expressed as 0.89, so to calculate the change of the population, we must each year multiply the number of cheetahs by 0.89.

After 1 year:     1750 * 0.89 ≈ 1558

After 2 years:  1558 * 0.89 ≈ 1387

After 3 years:  1387 * 0.89 ≈ 1234

After 4 years:  1234 * 0.89 ≈ 1098

After 5 years:  1098 * 0.89 ≈ 977

After 6 years:  977 * 0.89 ≈ 870

After 7 years:  870 * 0.89 ≈ 774

After 8 years:  774 * 0.89 ≈ 689

After 9 years:  689 * 0.89 ≈ 613

After 10 years:  613 * 0.89 ≈ 546

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Combine like terms<br> 5y-8-y
    10·2 answers
  • Give the coordinates of the unknown vertex of JKLM and graph
    13·1 answer
  • Which conclusion can be derived from this scatter plot?
    13·1 answer
  • x y -2 3 -1 3 0 3 1 3 2 3 Which graph represents the function described in the table? A) A B) B C) C D) D
    13·2 answers
  • Multiply and simplify: –5gh4 • (–2g3h5)
    14·1 answer
  • 4. Find an equation of the line that is tangent to the graph of 4x + 2xy^2 +44 = y^3 at the point (-3,2).
    13·1 answer
  • Can some body help me?
    8·2 answers
  • ____% of $4 = $3<br> Find the percentage
    11·1 answer
  • Maths question is here<br> 9+92*12312
    9·2 answers
  • PLEASE HELP!! Theres two questions
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!