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
Readme [11.4K]
3 years ago
5

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

Mathematics
2 answers:
Klio2033 [76]3 years ago
7 0

Answer:

dy/dx = [1/ln(10)][(2x+6)/(x^2 +6x)]

Step-by-step explanation:

See attachment

WARRIOR [948]3 years ago
3 0

Answer:

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

Step-by-step explanation:

given

y = \log_{10}{(x^2+6x)}

using the property of log \log_ab=\frac{log_cb}{log_ca}, and if c =e,\log_ab=\frac{ln{b}}{ln{a}}, we can rewrite our function as:

y = \dfrac{\ln{\left (x^{2} + 6 x \right )}}{\ln{\left (10 \right )}}

now we can easily differentiate:

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{d}{dx}(\ln{(x^{2} + 6x)})\right)

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{2x+6}{x^{2} + 6x}\right)

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

This is our answer!

You might be interested in
Use scientific notation to estimate the number of inches in 1,225 miles
madam [21]
First, find the number of inches
<span>1225 Miles = 77616000 Inches

then, move the decimal to until you have a ones place.    </span>
<span>77616000.    the decimal for this number moves to the left SEVEN places.
you end up with 7.7616000
</span>
it will look like this:

7.8 * 10^7

I rounded to the .8 because you didn't state how many significant figures, but it could easily be 7.76 * 10^7

the exponent above the 10 will tell you how many places to move. to get back to your original number, move it back to the right seven places. Of course, you would have to place hold the numbers with 0s. If it were negative, you would move the decimal the opposite way.
6 0
3 years ago
28. Express 22.7 : 45.4 as a single decimal
maria [59]

Answer:

0.5

Step-by-step explanation:

22.7: 45.4 = 22.7/45.4

                 = 227/454

                 = 0.5

4 0
2 years ago
Read 2 more answers
1 inch = 2.54 centimeters. How many centimeters long is an 18-inch ruler?
ArbitrLikvidat [17]

Answer:

45.72 cm

2.54 x 18

3 0
3 years ago
Read 2 more answers
write an equation in slope intercept form of a line passing through the point (2,-3) that is perpendicular to a line whose slope
vladimir2022 [97]
1) find slope. when its perpendicular, It will be a negative reciprocal to the given slope so m1= -1/m1 
m=-1

2) y=mx+b
    y =-1x+b 
    (-3)=-1(2)+b
     -3=-2+b
       b=-1

3)  y=-1x-1

hope I helped!
6 0
3 years ago
How do you calculate the area of triangle DEF?
cricket20 [7]
First you need to solve for angle F then you can use 1/2acSinB. If you haven't done this you can also use the Pythagoras theorem and solve for the unknown side once you do that you can just use 1/2 b*h
8 0
3 years ago
Read 2 more answers
Other questions:
  • There are 546 people attending a charity event you are baking cookies to give away each batch makes 48 cookies estimate the numb
    9·1 answer
  • Kyoko has completed 26 hours of community service. Her goal is to complete at least 90 hours this semester. Write and solve an i
    10·2 answers
  • How to find the area of a trapezium given:
    9·1 answer
  • This is sooo confusing
    12·2 answers
  • What is the percent for 5/4
    10·1 answer
  • Determine the domain of the function in the picture below
    11·1 answer
  • Doc decides to buy the entire 6th grade a slice of pizza.
    5·2 answers
  • If a1=<br> 1 and an=<br> (an-1)^2 + 2 then find the value of a4
    6·2 answers
  • I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. Find the area of t
    13·1 answer
  • An associate professor of physics gets a $200 a month raise. She figures that with her new monthly salary she can buy more goods
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!