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
Phoenix [80]
2 years ago
6

1. Differentiate with respect to x:​

Mathematics
1 answer:
natta225 [31]2 years ago
5 0

9514 1404 393

Answer:

  a) y' = x^2(3x·ln(6x) +1)

  b) y' = 6e^(3x)/(1 -e^(3x))^2

Step-by-step explanation:

The applicable rules for derivatives include ...

  d(u^n)/dx = n·u^(n-1)·du/dx

  d(uv)/dx = (du/dx)v +u(dv/dx)

  d(e^u)/dx = e^u·du/dx

  d(ln(u))/dx = 1/u·du/dx

__

(a)

  y=x^3\ln{(6x)}\\\\y'=3x^2\ln{(6x)}+\dfrac{x^3\cdot6}{6x}\\\\\boxed{\dfrac{dy}{dx}=3x^3\ln{(6x)}+x^2}

__

(b)

  y=\dfrac{1+e^{3x}}{1-e^{3x}}=1+\dfrac{2}{1-e^{3x}}=1+2(1-e^{3x})^{-1}\\\\y'=-2(1-e^{3x})^{-2} (-3e^{3x})\\\\\boxed{\dfrac{dy}{dx}=\dfrac{6e^{3x}}{(1-e^{3x})^2}}

You might be interested in
Can u guys help me with #1 plz guys now
myrzilka [38]
3

the area is 41.6cm which is 1foot  4 3/8 inches.

So 6in + 6in + 6in = 1ft 6in, which will be enough to cover the floor.
3 0
3 years ago
What is the average of -2.6, 1.8, -3.3, -2.7, 2.2 ?<br> I dont understand this.
olya-2409 [2.1K]
Average = Mean

To find the mean, add up the numbers and divide it by how many numbers there are.

So,  -2.6+1.8+(-3.3)+(-2.7)+2.2=-4.6

There are 5 numbers in total.

-4.6 \div 5=-0.92

To do these types of division, ignore the decimal and add a 0 at the end.

So we can do:
-460\div5=-92

And put back the decimal.
Hope this helps :)
4 0
3 years ago
Henry needs 2 pints of red paint and 3 pints of yellow paint to get a specific shade of orange. If he uses 9 pints of yellow pai
kkurt [141]
<span>I know because 2:3 is the ratio for the first and when he gets 9 that is 3* more. So we multiply 3*2 of the red paint and we will get 6 </span>
6 0
2 years ago
Read 2 more answers
anyone know thus multiple question.... yes you , i know you've saw this , your reading now ... please help (if you can of course
Bogdan [553]

where is the ques

pls say the ques

4 0
3 years ago
In order to solve the equation -3x - 6 = 5, the first step is to?
lions [1.4K]

Answer:

Add 6 by both sides

Divide both sides by - 3

4 0
3 years ago
Other questions:
  • The slope of a line is -4 and it’s y-intercept is (0,4) what is the equation of the line that is perpendicular to the first line
    15·1 answer
  • Which point is the best approximation of the relative maximum of the polynomial function graphed below?
    7·2 answers
  • 21,985,233 rounded to the millions place
    12·1 answer
  • 7) Find the sample standard deviation. 22 29 21 24 27 28 25 36​
    11·1 answer
  • Select the equation in which the graph of the line has a negative slope, and the y-intercept equals -8
    5·1 answer
  • Simplify x 2  − 4x + 4 x 2  − 4
    10·1 answer
  • What is the educated guess in mathematics
    13·1 answer
  • Two numbers have difference of 0.7 and a sum of 1. What are the numbers?
    6·1 answer
  • The distance between two cities is 180km. The distance was covered by a car at the rate of 50km/h, by a bus 45km/h, by a truck a
    12·1 answer
  • 12x-5y= -20<br><br> y=x+4<br><br> x=<br><br> y=
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!