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
arsen [322]
3 years ago
13

What is the first and second derivative of xe^(2x)?

Mathematics
2 answers:
astra-53 [7]3 years ago
6 0
The derivative of a function <span>xe^(2x) can be determined by applying differential calculus techniques to the equation. In this case, the applicable law is the law of products

</span><span>y = xe^(2x)
y' = 2x  e^2x + e^2x
y'' = 4x e^2x + 2e^2x + 2 e^2x
Simplifying
y'' = (4x+4) e^2x </span>
Nimfa-mama [501]3 years ago
5 0
f(x)=xe^{2x}\\\\f'(x)=x'e^{2x}+x(e^{2x})'=e^{2x}+xe^{2x}\cdot2=2xe^{2x}+e^{2x}=e^{2x}(2x+1)\\\\f''(x)=(e^{2x})'(2x+1)+e^{2x}(2x+1)'=e^{2x}\cdot2(2x+1)+e^{2x}\cdot2\\\\=e^{2x}(4x+2)+2e^{2x}=(4x+2+2)e^{2x}=(4x+4)e^{2x}\\\\Answer:\\\boxed{f'(x)=(2x+1)e^{2x}\ and\ f''(x)=(4x+4)e^{2x}}
You might be interested in
Find the rate of change of total​ revenue, cost, and profit with respect to time. Assume that​ R(x) and​ C(x) are in dollars. ​R
tresset_1 [31]

Answer:

Step-by-step explanation:

Given the Total revenue R(x) = 2x

Cost C(x) = 0.01x²+0.3x+30 where;

x = 30 and dx/dt = 9units per day.

Rate of change of revenue dR/dt = dR/dx • dx/dt

dR/dt = 2dx/dt

dR/dt = 2(9) = $18

Rate of change of revenue with respect to time is 18dollars/day.

Rate of change of cost dC/dt = dC/dx • dx/dt

dC/dt = (0.02x+0.3)dx/dt

dC/dt at x = 30 and dx/dt = 9 will give;

dC/dt = {0.02(30)+0.3}×9

dC/dt = (0.6+0.3) × 9

dC/dt = 0.9×9

dC/dt = $8.1

Rate of change of cost with respect to time is 8.1dollars/day

Profit = Revenue - Cost

Profit = 18-8.1

Daily Profit = $9.9

4 0
3 years ago
Which of the following describes the end behavior of y = -x^2+bx+c as x approaches either positive or negative infinity?
Pavlova-9 [17]
The end behavior model of y is -x^2.
As x approaches either positive or neg infinity, -x^2 will always be negative.
Thus, "B) y approaches neg infinity" is the correct one. 
Hope that will help :))

5 0
3 years ago
Triangle XYZ has vertices X(0,3), Y(2,0) and Z(4,2). if yo reflect triangle XYZ across the line x=4, what will be the coordinate
Paha777 [63]

As X' is the reflected point of X(0,3) , so the x co ordinate of X' = 0+8 =8 and here y co ordinate remains same.

So, X'= (8,3)

Like that way, Y' is the reflected point of Y(2,0) and Z' is the reflected point of Z(4,2)

As the point Z is lying on the line x=4 and the reflection is also across that line, so both Z and Z' represent same point.

Y'= (2+4, 0) = (6, 0)

Z' = (4, 2)

3 0
3 years ago
Simplify.<br><br> 38√<br><br><br><br><br> 3√4<br><br> 6√8<br><br> 24√8<br><br> 6√4
Naya [18.7K]

Answer:

the first one i believe

Step-by-step explanation:

hope this helps

5 0
3 years ago
A survey finds that 40% of students ride in a car to school. Eri would like to estimate the probability that if 3 students were
Butoxors [25]
The answer is 0.60 I know cause I took the test
3 0
3 years ago
Read 2 more answers
Other questions:
  • se the drawing tool to form the correct answers on the provided grid. For the sequence (1, 2, 4, 8, . . .), the index starts at
    7·1 answer
  • Is the dilation above an enlargement or a reduction
    12·1 answer
  • Find measure dbc <br> 19<br> 22<br> 23<br> 161 <br> HELP !!!
    10·1 answer
  • A suppose price per person for an event. If 17 people sign up. And the price per person is 213 what will be the price per person
    14·2 answers
  • Sara sells beaded necklaces she makes a profit of 4 dollars pn every neclace she sells which table represents the profit sara ma
    14·1 answer
  • Recap me ok area of circle the formula of
    11·2 answers
  • A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two
    10·1 answer
  • Hi<br><br>answer correct and I will follow you​
    12·1 answer
  • Find each product.<br> (2.05).(0.004)
    12·1 answer
  • Who created Sports Illustrated?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!