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
ivann1987 [24]
3 years ago
8

Let f(x)=(x^2)(e^5x) find the derivative f'(x) and the second derivative, f"(x)

Mathematics
2 answers:
Wittaler [7]3 years ago
7 0
F ` ( x ) = ( x² )` · e^(5x) + x² · ( e^(5x) )` =
= 2 x · e^(5x) + 5 e^(5x) · x² =
= x e^(5x) ( 2 + 5 x )
f `` ( x ) = ( 2 x e^(5x) + 5 x² e^(5x) ) ` =
= ( 2 x ) ˙e^(5x) + 2 x ( e^(5x) )` + ( 5 x² ) ` · e^(5x) + ( e^(5x)) ` · 5 x² = 
= 2 · e^(5x) + 10 x · e^(5x) + 10 x · e^(5x) + 25 x² · e^(5x) =
= e^(5x) · ( 2 + 20 x + 25 x² ) 
Nostrana [21]3 years ago
5 0
<span>Use the product rule! f(x) = (x^2)(e^5x) First times the derivative of the second, plus, second times the derivative of the first: (d/dx) f(x) = (x^2) d/dx(e^5x) + (e^5x) d/dx (x^2) what's the derivative of e^5x? well you have to chain rule for that: d/dx (e^5x) = (e^5x) (5) now what is the derivative of x^2? yup! just 2 d/dx (x^2) = 2 so what's f'(x)? Let's just plug in our derivatives f'(x) = (x^2) (e^5x) (5) + (e^5x)(2) tada!</span>
You might be interested in
Solve the literal equation a+4b=5b-3a solve for a
ahrayia [7]
A= 0.25 or 1/4
Hope this helps:)
4 0
3 years ago
A bag contains 5 red, 6 green, 7 yellow, and 8 blue jelly beans. A jelly bean is selected at random. What is the probability tha
Slav-nsk [51]

Answer:

4/13 is the probability does a blue Jelly Bean is selected

Step-by-step explanation:

sample space = sum of all the jelly beans in the bag

sample space =5+6+7+8

sample space =26

probability = Jelly Bean selected / sample space

probability =8/26

probability =4/13

4 0
3 years ago
You have two summer jobs. At the Burger Palace you earn $8 per hour. At the community center you teach soccer clinics for $10 pe
SIZIF [17.4K]
The complete question in the attached figure
 we have that
x-------------> number of hours works at Burger Palace -----> <span>$8
</span>y-------------> number of hours works at <span>community center</span> -----> $10
<span>
8x+10y>=200

using a graph tool
see the attached figure

the answer is the option B
</span><span>
</span>

8 0
3 years ago
X/-9 + n/-7 = 9<br> solve for x
Andrews [41]

9514 1404 393

Answer:

  x = -(9/7)n -81

Step-by-step explanation:

Subtract the n term.

  x/-9 = 9 -n/-7

Multiply by -9.

  x = -81 -(9/7)n

6 0
2 years ago
5^2= (-5)^2 <br> true or false
Nonamiya [84]
It’s True because of 5 square is equal to 25
Than (-5) square is also get the same value as 5^2
8 0
3 years ago
Other questions:
  • How to solve and what is the answer
    10·1 answer
  • 1 plus 1 is a 1 b3 c5 d2
    8·2 answers
  • 3*4-1*2 simplest form
    10·1 answer
  • Mrs. Okafor had $475 in her savings account. Each year, the value of the savings account increases
    6·1 answer
  • Find the area of the figure.
    15·2 answers
  • How many different numbers between $\dfrac{1}{1000}$ and $1000$ can be written either as a power of $2$ or as a power of $3$, wh
    11·2 answers
  • Write an equivalent expression to
    8·1 answer
  • What is the y-intercept of the line graphed on the grid?
    13·2 answers
  • -"7x + 9 In the expresion show, which of the following is the coefficient?
    8·2 answers
  • Referring to the figure, find the area of the<br> trapezoid shown.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!