Hello! :)
[tex]\large\boxed{\frac{-e^{\frac{3}{x}} (3 + 2x )}{x^{4}}}[/tex]
Find the derivative using the quotient rule:
[tex]\frac{f(x)}{g(x)} = \frac{g(x) * f'(x) - f(x) * g'(x)}{(g(x))^{2}}[/tex]
In this instance:
[tex]f(x) = e^{\frac{3}{x} }\\\\g(x) = x^{2}[/tex]
Use the following properties to find the derivative of f(x) and g(x):
[tex]e^{u} = u' * e^{u}\\\\x^{n} = nx^{n-1}[/tex]
Use the quotient rule:
[tex]\frac{x^{2} * (e^{\frac{3}{x}} * (-3x^{-2})) - e^{\frac{3}{x}} * 2x }{(x^{2} )^{2}}[/tex]
Simplify the numerator:
[tex]\frac{(e^{\frac{3}{x}} * (-3)) - e^{\frac{3}{x}} * 2x }{(x^{2} )^{2}}[/tex]
Factor out [tex]e^{\frac{3}{x}}[/tex]
[tex]\frac{e^{\frac{3}{x}} (-3 - 2x )}{x^{4}}[/tex]
Factor out -1 from the numerator:
[tex]\frac{-e^{\frac{3}{x}} (3 + 2x )}{x^{4}}[/tex]
And we're done! Thanks for posting the question to my 1000th answer!
Answer:
[tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}}}{x^4} - \frac{2e^{\frac{3}{x}}}{x^3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Splitting FractionsAlgebra I
Terms/CoefficientsFactoringExponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule: [tex]\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'[/tex]
Quotient Rule: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{e^{\frac{3}{x}}}{x^2}\\f(x) = e^{\frac{3}{x}}\\g(x) = x^2[/tex]
Step 2: Differentiate
Quotient Rule: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{\frac{d}{dx}[e^{\frac{3}{x}}] \cdot x^2 - \frac{d}{dx}[x^2] \cdot e^{\frac{3}{x}}}{(x^2)^2}[/tex]Derivative Rule: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{e^{\frac{3}{x}} \cdot \frac{-3}{x^2} \cdot x^2 - \frac{d}{dx}[x^2] \cdot e^{\frac{3}{x}}}{(x^2)^2}[/tex][Simplify] Multiply: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}} - \frac{d}{dx}[x^2] \cdot e^{\frac{3}{x}}}{(x^2)^2}[/tex]Basic Power Rule: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}} - 2x^{2-1} \cdot e^{\frac{3}{x}}}{(x^2)^2}[/tex][Simplify] Subtract Exponents: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}} - 2x \cdot e^{\frac{3}{x}}}{(x^2)^2}[/tex][Simplify] Multiply: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}} - 2xe^{\frac{3}{x}}}{(x^2)^2}[/tex][Simplify] Exponent Rule: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}} - 2xe^{\frac{3}{x}}}{x^{2 + 2}}[/tex][Simplify] Add Exponents: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}} - 2xe^{\frac{3}{x}}}{x^4}[/tex][Simplify] Fraction Split: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}}}{x^4} - \frac{2xe^{\frac{3}{x}}}{x^4}[/tex][Simplify - 2nd Fraction] Cancel Like Terms: [tex]\displaystyle \frac{d}{dx}[\frac{e^{\frac{3}{x}}}{x^2}] = \frac{-3e^{\frac{3}{x}}}{x^4} - \frac{2e^{\frac{3}{x}}}{x^3}[/tex]And we have our final answer!
What is 100% of 7344
7344
4622
15,642
3672
Answer:
7344
Step-by-step explanation:
Answer:
the answer is 7344 mark brainliest
what is -4 (-6x + 3) = 12
Answer: x = 1
Step-by-step explanation:
Simplifying
-4(-6x + 3) = 12
Reorder the terms:
-4(3 + -6x) = 12
(3 * -4 + -6x * -4) = 12
(-12 + 24x) = 12
Solving
-12 + 24x = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '12' to each side of the equation.
-12 + 12 + 24x = 12 + 12
Combine like terms: -12 + 12 = 0
0 + 24x = 12 + 12
24x = 12 + 12
Combine like terms: 12 + 12 = 24
24x = 24
Divide each side by '24'.
x = 1
Simplifying
x = 1
Answer:
Step-by-step explanation: heyy... the pic attached below shows all the steps with a brief explanation. I hope it helps u !!!
Use the distributive property to remove the parentheses.
4(x-7)
Please give a step by step answer if possible
Divide each term in
4
x
=
7
by
4
.
4
x
4
=
7
4
Cancel the common factor of
4
.
Tap for more steps...
x
=
7
4
The result can be shown in multiple forms.
Exact Form:
x
=
7
4
Decimal Form:
x
=
1.75
Mixed Number Form:
x
=
1
3
4
How does the graph of f(x) = |x| compare with the graph of g(x) = −2|x|? Select all that apply.
A. The graph of g is a vertical compression of the graph of f.
B. The graph of g is a vertical stretch of the graph of f.
C. The graph of g is a reflection over the x-axis of the graph of f.
Answer:A
Step-by-step explanation:
Using translation concepts, it is found that the corrects options are:
B. The graph of g is a vertical stretch of the graph of f.
C. The graph of g is a reflection over the x-axis of the graph of f.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.In this problem, the functions are:
[tex]f(x) = |x|[/tex]
[tex]g(x) = -2|x|[/tex]
g is the function of f multiplicated by -2, hence:
It is a vertical stretch, as it is multiplied by a value with absolute value greater than 1.It is multiplicated by a negative value, hence it is reflected over the x-axis.Hence, options b and c are correct.You can learn more about translation concepts at https://brainly.com/question/13671886
What is the slope of the line?
Answer:
- 7/4
Step-by-step explanation:
1) (y2 - y1)/(x2 - x1)
2) pick two points, mine were (1,-3) and (-3,4)
3) Substitute the values (4+3)/(-3-1)
4) Solve and no matter what points you’ll get -7/4
Solve the system.
2x + 3y – z = -1
6. x - 2y + 4z = 18
(5x + 6y – 2z = -6
Answer:
x=-4
y=7
z=14
Step-by-step explanation:
Write an equation of the line that passes through (4,-2) and is parallel to y=1/2x -7
Answer:
5 x - 6 y - 8 = 0.
Step-by-step explanation:
(0,0)
M is the midpoint of CD. If the midpoint M
is (-3, 5) and C is (2,3), then what are the
coordinates of D?
O
(-1/2,4)
(-8,7)
o
(-4,1)
Answer:
The answer is (3-,5) watch is C cause if you do that but in math form it's the same
Factor the polynomial f (x) = x3 – 19x + 30 if x – 3 is a factor.
Answer:
Step-by-step explanation
By Using Synthetic Division Method:
3 1 0 -19 30
3 9 -30
1 3 -10 0
factorise: (x^2+3x-10)(x-3)
=(x+5)(x-2)(x-3)
Answer:
ITs B on edge
Step-by-step explanation:
cause i said so cuzzzz
what are the zeros of the polynomial x squared+5x+6
Answer: (-3, 0) and (-2, 0)
Step-by-step explanation:
1. Factor
(x+3)(x+2) = 0
2. Check if your factoring is correct
x^2 + 3x +2x + 6 = 0
x^2 + 5x + 6 = 0
3. Look back at factors and use them to find the zeros
(x+3) - > (-3, 0)
(x+2) -> (-2, 0)
Consider the equation x-5) =(y-2)2. What is the equation of the directri?
Hurry 20 points
What is the first step in the standard construction of the perpendicular bisector of MN¯¯¯¯¯¯¯ ?
A.
Use a straightedge to draw a line perpendicular to line segment MN¯¯¯¯¯¯¯ .
B.
Use a straightedge to draw a line parallel to line MN¯¯¯¯¯¯¯.
C.
Use a compass to draw one arc with point M at the center and intersecting point N.
D.
Use a compass to draw two intersecting arcs with centers at points M and N.
Answer:
C. Use a compass to draw one arc with point M at the center and intersecting point N.
Step-by-step explanation:
I took the test and got it right.
Your welcome :)
Using a compass, draw one arc with point M at the center and point N intersecting it as the first step in the typical construction of the perpendicular bisector of MN. Option C is correct.
What are perpendicular bisectors?Lines that cut through the middle of each side of a triangle and are perpendicular to the specified side are known as the perpendicular bisectors of the triangle.
The standard construction of the perpendicular bisector of MN will be,
Step 1: Sketch a line segment with any appropriate length, XY.
Step 2: Using a compass, draw arcs above and below the line segment, with X serving as the center and XY's width greater than 50%.
Step 3: Carry out Step 2 but use Y as the center. Step 4: Write "P" and "Q" next to the junction points.
Thus, using a compass, draw one arc with point M at the center and point N intersecting it as the first step in the typical construction of the perpendicular bisector of MN. Option C is correct.
Learn more about the perpendicular bisectors here,
https://brainly.com/question/24753075
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What is the rate of change of the function y= -7?
Answer:
Zero
Step-by-step explanation:
Average rate of change can also be called as gradient or change in the respective variable , in this case we need the average rate of change of y which has the function y = -7
Since this is a linear function and if we draw the graph of y = -7 the graph would be parallel to the x-axis, and any line parallel to the x-axis has slope of zero , hence the average rate of change of the function y = -7 is zero
The price of a ticket, in dollars, on the local commuter train can be determined from the expression 2.75 + 0.50(s), where s is the number of stops for which the passenger will be on the train. Use this expression to find the price of a ticket to ride the train for 13 stops.
Answer:
$9.25
Step-by-step explanation:
2.75+ .5(13)
.50 (13)= 6.5
6.5 +2.75= 9.25
Jenna made money babysitting, and she also earned $20 cleaning her neighbor's basement. During the week, her total earnings were $55. If she charges $5 per hour for babysitting, how many hours did she babysit?
Answer:
Jenna spent 7 hours babysitting.
Step-by-step explanation:
With the information provided, you can say that Jenna's total earnings are equal to the amount she earned cleaning her neighbor's basement plus the result of multiplying the charge per hour for babysitting for the number f hours, which is:
e=20+5x, where:
e represents the total earnings
x is the number of hours
Now, you can replace e with 55 that is the toal amount she earned and solve for x:
55=20+5x
55-20=5x
35=5x
x=35/5
x=7
According to this, the answer is that Jenna spent 7 hours babysitting.
The height of a building is 1417 ft. How long would it take an object to fall to the ground from the top? Use the formula s = 16t ^ 2 where s is the distance, in feet traveled by an object falling freely from rest in seconds.
Given :
The height of a building is 1417 ft.
To Find :
How long would it take an object to fall to the ground from the top.
( Use the formula s = 16t² where s is the distance, in feet traveled by an object falling freely from rest in seconds. )
Solution :
Putting value of height in given equation, we get :
[tex]16t^2 = 1417\\\\t^2 = \dfrac{1417}{16}\\\\t^2 = 88.5625\\\\t = \sqrt{88.5625}\\\\t = 9.41 \ seconds[/tex]
Therefore, time taken by object to reach the ground is 9.41 seconds.
Which of the following conditions is necessary to prove that a quadrilateral is a parallelogram?
A. the diagonals bisect each other
B. The diagonals are congruent
C. The diagonals are perpendicular
D. The diagonals intersect on the perpendicular bisector of the two sides?
PLEASE HELP NEED HELP ASAP!!!!!!
Answers:
x = 3
y = 9
=========================================================
Explanation:
We're told that angle A is 20x. The diagram shows we have an equilateral triangle (since all three sides are the same length), so we know that all angles are the same measure and they are equal to 60 degrees.
Equate 20x and 60. So we solve 20x = 60 and that leads to x = 3 after you divide both sides by 20.
Since we have a triangle with all sides equal, we know that AB = AC = 9, therefore y = 9 because y is the length of AB.
Help mee cuz if you help me I will give you brain last
Answer:
it is c
Step-by-step explanation:
Ajit says the following steps can be used to find 0.48 of in which step did he make his first error? Step 1 Change "of" to the multiplication symbol. O Step 1 O Step 2 O Step 3 Step 2 48 x 7 = 336 O Step 4 Step 3 There is 1 decimal place in 7 and 3 decimal places in 0.48 for a total of 4 decimal places in the factors Step 4. Move the decimal place in the product 4 places to the left to find the solution: 0.48 of 7 is 0.0336.
Answer:
step one
Step-by-step explanation:
of is a key word for division
3/8 divided by 2/3.
Answer:
Fraction: 9/16
Decimal: 0.563
What is the percent of change from 5,000 to 9,000?
Answer:
40%
Step-by-step explanation:
10000 = 5000 = 50% + 9000 = 40%
Can someone really help me please
Answer: 22
Step-by-step explanation:
How do you solve quadratic equations?
Answer:
Completing the square
Put the equation into the form ax 2 + bx = – c.
Make sure that a = 1 (if a ≠ 1, multiply through the equation by. before proceeding).
Using the value of b from this new equation, add. ...
Find the square root of both sides of the equation.
Solve the resulting equation.
Step-by-step explanation:
there
Answer: Put the equation into the form ax 2 + bx = – c.
Make sure that a = 1 (if a ≠ 1, multiply through the equation by. before proceeding).
Using the value of b from this new equation, add.
Find the square root of both sides of the equation.
Solve the resulting equation.
Step-by-step explanation: Hope this helps!
Which values from this set {−30, −20, −10, 0, 10, 20} satisfy this inequality?
−1/5x+3 ≤ 7
please solve asap im so confused
Answer:
Step-by-step explanation:
-1/5 x+3 ≤7
-1/5 x≤7-3
-1/5 x≤4
x≥-20
{-20,-10,0,10,20}
!!!!!!!!!!!!!!!!!!!!!!!
Answer:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
A shop is offering a 15% reduction on the price of a computer .The original price of the computer was $670.what is its reduced price?
Answer:
$569.50
Step-by-step explanation:
15% deduction from the initial price(100%) will have us remaining with 85%
100% = 670
85% = 85% x 670
100%
= $569.50
20pts answer please the picture
Answer: Hope this helps!
Step-by-step explanation:
Area of a trapezoid formula base a+base b/2*h
Base a is the top length (22.5)
Base b is the bottom length (49.9)
Add those two lengths together (22.5+49.9=72.4)
Divide that by two (72.4/2=36.2)
Then multiply that by the height (36.2*23.8=861.56)
So your area is 861.56
What is the slope of a ski run that rises 5 feet for every horizontal change of 20 feet? Pls show work
Answer: -1/4
Step-by-step explanation: The slope is rise over run. The ski run drops 5, so it would be -5, and the horizontal change of 20 would be the run, so you'd get -5 over 20 then you divide both by 5 and you get your answer of -1 over 4.
-1/4 is the slope of a ski run that rises 5 feet for every horizontal change of 20 feet
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given the slope of a ski run that rises 5 feet for every horizontal change of 20 feet
So the two points are (0,5) and (20,0)
m=0-5/20-0
m=-5/20
m=-1/4
Hence -1/4 is the slope of a ski run that rises 5 feet for every horizontal change of 20 feet
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what percent of 120 is 66?
Answer:
55%
Step-by-step explanation:
66
120
x 100% = 55%
Answer:
66 is 55% of 120
Step-by-step explanation:
66 = 120 * x%
percent just means out of 100
for example, 20% is equal to 20/100
so, x% is x/100
66 = 120 * x/100
66/[tex]\frac{x}{100}[/tex] = 120
66 * 100/x = 120
6600/x = 120
cross multiply
6600/x = 120/1
6600 * 1 = x * 120
6600/120 = x
x = 55