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
Sana's mother bought produce for Sunday dinner. She bought one more pound of peaches than of tomatoes. She bought 3 times as man
Elenna [48]

1(Identifying):

Tomatoes-x--$3 per lb

Mushrooms- 1/3 x-- $10 per lb

Peaches- x+1-- $6 per lb

2(Equation):

3x+6(x+1)+1/3x*10=80

3x+6x+6+10/3 x=80

12 1/3 x= 74

x=74÷(12+1/3)

Step 3(Final Equations):

74*3/37=6=tomatoes

Meaning...

6+1=7=Peaches

6/3=2= mushrooms

Answer:

7 lb of peaches, 6 lb of tomatoes, and 2 lb of mushrooms

7 0
2 years ago
Read 2 more answers
Can someone please tell me why I got this wrong?
kvasek [131]
We have 
f(x)=<span>−x</span>²<span>+ 5x + 6
g(x)=</span><span>3x − 2

we know that
f(x)=g(x)
the solution is the intersection both graphs

using a graph tool
see the attached figure

the solution are the points
(4,10)
and
(-2,-8)

</span>

8 0
2 years ago
An open box is to be made from a flat square piece of material 16 inches in length and width by cutting equal squares of length
vaieri [72.5K]

Answer:

V = x(19-2x)(4-2x)

Step-by-step explanation:

We are given;

Length of flat piece of material =19 inches

Width of flat piece = 4 inches

We are told that the open box is to be made from a flat piece by cutting equal squares of length x from the corners and folding up the sides

Thus, we will now have;

length of open box = (19-2x) inches

Width of open box = (4-2x) inches

Height of box = x inches

We know that: Volume of box = length × width × height

So, plugging in the relevant values, we have;

Volume of box(V) = x(19-2x)(4-2x)

7 0
3 years ago
a used automobile dealership recently reduced the price of a used compact car by 10 % if the price of the car before discount wa
Delvig [45]

Answer: The new price is $3350.


8 0
3 years ago
Read 2 more answers
Nine students Ryan’s class are wearing gray there are 30 students in his class Ryan says that 30% of his class is wearing gray i
aleksklad [387]

Answer:

ur mom

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the difference between 20 and -60
    6·1 answer
  • Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of tr
    12·1 answer
  • Andrew ate 1/3 of a pumpkin pie. sarah ate 1/6 of the pie. how much pie is left?
    5·1 answer
  • PLEASE HELP PICTURE IS SHOWNNN !!!!GEOMETRY
    9·1 answer
  • I need help with this one too. Please!!
    9·2 answers
  • If x=9 and y=3 then |1-2x|+4y^2
    5·1 answer
  • Solve for the missing angle with the question mark
    7·1 answer
  • For the problem I see posted here already that reads - " A woman has two bank accounts. One contains $329 and awards 4% in inter
    14·1 answer
  • Find the slope of -3/5x-1
    8·1 answer
  • How do I solve this? i missed ONE class
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!