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
puteri [66]
3 years ago
8

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Mathematics
1 answer:
wlad13 [49]3 years ago
8 0

Answer:

\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}

Step-by-step explanation:

To solve the question we refresh our knowledge of the quotient rule.

For a function f(x) express as a ratio of another functions u(x) and v(x) i.e

f(x)=\frac{u(x)}{v(x)}\\, the derivative is express as

\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }

from y=lnx/x^{2}

we assign u(x)=lnx and v(x)=x^2

and the derivatives

\frac{du(x)}{dx}=\frac{1}{x}\\\frac{dv(x)}{dx}=2x\\.

Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e y=lnx\\\frac{dy}{dx}=\frac{1}{x}

If we substitute values into the quotient expression we arrive at

\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}

You might be interested in
Dont guess!<br> I will mark brainliest if its correct!<br> Also no links!
GREYUIT [131]

Answer:

The correct answer will be; B or 40.

Step-by-step explanation:

Because when the ratio of boys changed from 8 to 32, it increased by "time 4" (8*4 = 32), so the same pattern will be followed for girls, multiplying the number that you already have by four; 10 (amount of girls given) * 4 = 40.

Hope this helped, Good Luck!

8 0
3 years ago
Read 2 more answers
What is the value of x in the diagram below? 2 right triangles are stacked. The bottom triangle has a side length of 9 units and
ehidna [41]

Answer:

18 sqrt2/ sqrt3

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Value of sin^6 + cos^6+3sin^2cos^2 ​
Sav [38]

Step-by-step explanation:

If you put into a calculator "Sin(6)+Cos(6)+3Sin(2)Cos(2)", you get 1.20368506925. Hope that helps

4 0
3 years ago
Which expressions are equivalent to 2 (a + 3b)?
VARVARA [1.3K]

Answer:

A & B

Step-by-step explanation:

A is spot-on because of the use of distributive property. B by the use of like terms.

8 0
3 years ago
The diameter of a building's dome is 82 feet at its widest point. Find its circumference. Round to the nearest tenth. Use 3.14 f
andreyandreev [35.5K]

Answer:

257.5 ft

Step-by-step explanation:

circumference of a circle with diameter=

pi*d

3.14*82=257.48

Hope this helps!

7 0
3 years ago
Read 2 more answers
Other questions:
  • Simply the following.
    8·1 answer
  • PLS ANSWER I NEED HELP ILL GIVE 50 POINTS PLS NO ONE HELPS ME.
    7·2 answers
  • Help me please, kinda lost
    11·1 answer
  • Simplify the expression. (5x2 - x - 7) + (2x2 + 3x + 4)
    9·1 answer
  • In “modeling with linear equations” how do i solve<br><br> -11-8x=-3x+19
    14·1 answer
  • Pls helpppp lol :/ I’d really appreciate it !!
    13·1 answer
  • Circle D is shown. Line segment F E goes through point D. Line segment C D is shown. Line segment G H goes from one side of the
    9·2 answers
  • I Neeedd it quickk pleasee anyonee helpp
    14·2 answers
  • What is $76,186 as a percent
    12·1 answer
  • Gary and Jessica exercise for a total of 18 hours per week. Jessica exercises 2 less than 3 times the hours that Gary exercises.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!