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
balandron [24]
3 years ago
9

Log_{7 }(5 - 3x)Find the derivative​

Mathematics
1 answer:
V125BC [204]3 years ago
6 0

Let <em>y</em> be the expression you want to differentiate:

y=\log_7(5-3x) \implies 7^y=5-3x

Now,

7^y=e^{\ln(7^y)}=e^{y\ln(7)}

Use the chain rule to differentiate both sides with respect to <em>x</em> :

\ln(7)e^{y\ln(7)}\dfrac{\mathrm dy}{\mathrm dx}=-3

Solve for d<em>y</em>/d<em>x</em> :

\ln(7)7^y\dfrac{\mathrm dy}{\mathrm dx}=-3

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac3{\ln(7)7^y}

\dfrac{\mathrm dy}{\mathrm dx}=\boxed{-\dfrac3{\ln(7)(5-3x)}}

You might be interested in
Find a set of parametric equations of the line with the given characteristics. (Enter your answer as a comma-separated list of e
emmainna [20.7K]

This question is incomplete, the complete question is;

Find a set of parametric equations of the line with the given characteristics. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) The line passes through the point (3, 1, 2) and is parallel to the line given by x  = y = z.

Answer:

the set of parametric equations of the line with the given characteristics are; x = t+3, y = t+1, z = t+2

Step-by-step explanation:

Given that;

line x = y = z and point ( 3, 1, 2 )

the given line can be written as;

[x-0 / 1] = [y-0 / 1] = [z-0 / 1]

if two lines are parallel directional ratios are equal.

so DIRECTIONAL RATIOS  of given line is ( 1, 1, 1 )

therefore required line is;

[x-3 / 1] = [y-1 / 1] = [z-2 / 1] = t

⇒ [x-3 / 1] = t

x = t+3

[y-1 / 1] = t

y = t+1

[z-2 / 1] = t

z = t+2

Therefore the set of parametric equations of the line with the given characteristics are; x = t+3, y = t+1, z = t+2

8 0
3 years ago
How does the graph of g(x) = -(x + 3)4 compare to the parent function of f(x) = xº?
AnnyKZ [126]

Answer:

g(x) is shifted 3 units to the left and reflected over the x-axis.

Step-by-step explanation:

8 0
3 years ago
Solve for x: −2x + 5 &lt; 7 <br> Please Help Meh!! DO you LIKE to see people STRUGGLE?!?!
Arlecino [84]

x > -1


-2x+5 < 7

-2x<2

Now since you divide by (-1) to get positive 2,you need to flip the sign

(-2)/(-1)= 2     2/(-1)=-2

SO

2x>-2

x > -1

To check  the solution do not replace the x by -1 because it shouls be more than -1  (You can choose 0,1,2,3....)

Example  choose x=3

-2x3+5<7

-6+5<7

-1<7

8 0
3 years ago
Find the pattern: 1, 1/4, 1/9, 1/16, 1/25
alexandr1967 [171]
The sequence is not geometric or arithmetic because there is no common difference or common ratio between each term.
Not a Geometric or Arithmetic Sequence
8 0
3 years ago
Hi pls answer I'll mark you brainliest​
OLEGan [10]
A) y= -2, 3, 7


B) y= 8, 0, -6


C) y= -8, 1, 7


d) y= 1, -2, -6

7 0
3 years ago
Read 2 more answers
Other questions:
  • Please answer correctly !!!! Will mark brainliest !!
    12·2 answers
  • Geri believed the answer to one of her homework problems was 2 cubed. After checking her work, she realized the correct answer w
    12·1 answer
  • What is 6/15 as a decimal
    6·2 answers
  • Linda has a shelf that is 56 over 5 inches wide. how many catalogs can linda arrange on the shelf if each catalog is 4 over 5 of
    8·2 answers
  • Gcf of 30x2,6x6,18x2
    14·1 answer
  • NEED HELP WITH TRIG MUST SHOW FULL WORK PLS
    14·1 answer
  • 9) Three times a number added to 12 gives -6. Find the number.​
    10·2 answers
  • 6sqrt20 + 8sqrt5 - 5sqrt45
    12·1 answer
  • (Can Someone Help Answer This Problem) + No Links
    12·2 answers
  • Carlos biked StartFraction 139 over 8 EndFraction miles on Saturday and StartFraction 135 over 7 EndFraction miles on Sunday. On
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!