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
Sveta_85 [38]
3 years ago
9

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

Mathematics
1 answer:
Tasya [4]3 years ago
5 0

Answer:

\frac{dy}{dx}=-[(\frac{5x+24}{36x-6x^2})]

Step-by-step explanation:

Given function:

y =\ln(\frac{(6 - x)^{\frac{3}{2}}}{x^{\frac{2}{3}}})

we know

\ln(\frac{A}{B}) = ln(A) - ln(B)

thus,

y = \ln((6 - x)^{\frac{3}{2}}) - \ln(x^{\frac{2}{3}})

or

also,

ln(Aⁿ) = n × ln(A)

thus,

y = (\frac{3}{2})\times\ln(6 - x) - (\frac{2}{3})\times\ln(x)

therefore,

\frac{dy}{dx}=[(\frac{3}{2})\times\frac{1}{(6-x)}\times(0 - 1)] - [ (\frac{2}{3})\times\frac{1}{x}\times1]

or

\frac{dy}{dx}=-(\frac{3}{2(6-x)}) - (\frac{2}{3x})

or

\frac{dy}{dx}=-[(\frac{3(3x)+2\times2(6-x)}{2(6-x)\times(3x)})]

or

\frac{dy}{dx}=-[(\frac{5x+24}{36x-6x^2})]

You might be interested in
I have one curved surface and one circle face. That's it.<br> I am a
svp [43]

Answer:

Cone

Step-by-step explanation:

The curved surface is the top part and the circular face is the bottom.

6 0
3 years ago
Read 2 more answers
Which is not an equation of the line going through (3, -6) and (1,2)
True [87]
Answer is A.
You can find the answer by plugging in X and Y to the equations




7 0
3 years ago
Read 2 more answers
What is the slope m, of the line passing through the points (2,3) (2,-3)
yan [13]

Answer:

Undefined

subtract your two points (y-y)/(x-x)

3 0
2 years ago
Read 2 more answers
How do you solve this problem in the photo?
Klio2033 [76]

Answer: 5^2

Step-by-step explanation:

Since the base are all the same, you will add the exponents and let the exponents stay the same.

5^3  * 5^4= 5^7 * 5^-5= 5^2

6 0
3 years ago
Read 2 more answers
Use the given graph to determine the period of the function. 1 &amp; 2 plz
White raven [17]
The period of the function is that distance where the function becomes equal again.
 We have then:
 Part 1:
 The period of the function is:
 T = 3
 Part 2:
 The period of the function is:
 T = 4
 Answer:
 
The period of functions 1 and 2 respectively are:
 
T = 3
 
T = 4
6 0
3 years ago
Other questions:
  • The measure of an angle is 8 degrees less than three times the measure of another angle. If the two angles are supplementary, wh
    14·1 answer
  • (4n+4)(5n-8)
    6·1 answer
  • Answer plz Nina has a collection of 20 seashells she wants to display in rows List all of the ways that nina can display her she
    10·1 answer
  • BRAINLIEST AND 50 PTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    6·1 answer
  • s<img src="https://tex.z-dn.net/?f=elect%20all%20of%20the%20following%20expressions%20that%20are%20equivalent%20to%204%E2%88%9A5
    6·1 answer
  • ∠A and ∠B form a linear pair. Find ∠A and ∠B if ∠A = 2∠B.
    7·1 answer
  • PLEASE HELP ME!!!!
    7·1 answer
  • Tell me if its blurry
    14·1 answer
  • Need help on this question
    5·1 answer
  • If RU = TU = 56 and RS = 87, what is ST?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!