find the first derivative of the following:
f(x)=e^{x³}
Answers
[tex]answer = 3 {x}^{2} {e}^{ {x}^{3} } [/tex]
Answer:
[tex] \displaystyle f'(x) = 3x^2 {e}^{ {x}^{3} } [/tex]
Step-by-step explanation:
we would like to figure out the first derivative of the following:
[tex] \displaystyle f(x) = {e}^{x ^{3} } [/tex]
to do so take derivative In both sides:
[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{x ^{3} } [/tex]
to differentiate the above we can consider composite function derivation given by
[tex] \rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dx} f'(g(x)) \times \frac{d}{dx} g'(x)[/tex]
let
g(x)=u
so we obtain:
[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{u} \times \frac{d}{dx} u[/tex]
substitute back:
[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{ {x}^{3} } \times \frac{d}{dx} {x}^{3} [/tex]
by using derivation rule we acquire:
[tex] \displaystyle f'(x) = 3x^2 {e}^{ {x}^{3} } [/tex]
and we are done!
Related Questions
Hunter is 9 years older than 3 times the age of his nephew.
Hunter is 33 years old. How old is his nephew?
Answers
Answer:
Hunter's nephew is 8 years old.
Step-by-step explanation:
We could set up an expression to represent the situation, then solve for the nephew's age. The age of the nephew should be represented by X.
3x + 9 = 33
To get 3x by itself, subtract 9 from both sides.
3x + 9 - 9 = 33 - 9
3x = 24
To get X alone, divide by 3 on both sides.
24 divided by 3 is 8. Hunter's nephew is 8 years old.
can someone help please !! giving brainlist to anyone who answers
Answers
Answer:
with?
Step-by-step explanation:
Question 3 of 10
What are the domain and range of the function represented by the table?
х
-5
0
5
10
15
|
у
-1
0
1
2
3
O A. Domain: -5 sxs 15
Range:{-1,0, 1, 2, 3}
O B. Domain: {-5, 0, 5, 10, 15}
Range: -1 sys3
O C. Domain: {-1,0, 1, 2, 3}
Range:{-5, 0, 5, 10, 15}
D. Domain:{-5, 0, 5, 10, 15)
Range:{-1,0, 1, 2, 3}
Answers
Given:
The table of values of a function.
To find:
The domain and range of the given function.
Solution:
Domain: The set of input values of x-values is known as domain.
Range: The set of output values of y-values is known as domain.
From the given table it is clear that x-values are [tex]-5,0,5,10,15[/tex] and the y-values are [tex]-1,0,1,2,3[/tex]. So,
[tex]Domain=\{-5,0,5,10,15\}[/tex]
[tex]Range=\{-1,0,1,2,3\}[/tex]
Therefore, the correct option is D.
The domain and range of the function represented by the table is as follows:
Domain: {-5, 0, 0, 5, 10, 15}Range: {-1, 0, 1, 2, 3}What are domain and range of a function?The domain of a function is the set of input values, x, for which a function is defined. The domain is the input of the function. The domain is the sets of all input value that produces the output value.
The domain are likewise called input . The domain are usually the x values
The set of values the function outputs is termed the range of the function. In a simpler term, the range are the output of the function. The range are usually the y values.
Therefore, the domain and range of the function represented by the table is as follows;
Domain: {-5, 0, 0, 5, 10, 15}Range: {-1, 0, 1, 2, 3}learn more on domain and range here; https://brainly.com/question/25173046
find the inverse function
Answers
Answer
[tex] {f}^{ - 1} (x) = \frac{5}{2} x - 5.[/tex]
Step by step
[tex]y = \frac{2x}{5} + 2[/tex]
Swap roles of x and y
[tex]x = \frac{2}{5} y + 2[/tex]
Then
[tex]5x = 2y + 10[/tex]
So
[tex]2y = 5x - 10[/tex]
Hence
[tex]y = \frac{5}{2} x - 5[/tex]
Therefore
[tex] {f}^{ - 1} (x) = \frac{5}{2} x - 5.[/tex]
GRADE 6 MATH PLEASE ANSWER DUE TOMORROW
Answers
Answer:
I left out a few so you can do 1 or 2! :D
Step-by-step explanation:
3: 1/2 hour + 1/4 hour= 3/4 hour on computer
5: 1/5 more of the money
6: 8/5 9/4
7: a:6 5/9 b: 3 9/10 c: 4/5 d: 4 5/8
8 They have the same denominator
10: a: 5/12 b: 6 times more c: How much of the day does he spend sleeping or schooling
Give Brainiest answer to me. It helps! :D
Answers:
4.)
a)
i) 3/8 - 1/4 = 3/8 - 2/8 = 1/8
ii) 4/5 - 3/4 = 16/20 - 15/20 = 1/20
b)
9.) It's less than 1 and the tops are smaller then the bottem
3)
How many solutions are there to the following equation?
3x-2(1 + x) + 2 = x
A. O
B. 1
C. Infinitely many
Answers
Answer:
letter B.1
ayan po sagot sa number 3
Step-by-step explanation:
3x-2(1 + x) + 2 = x
3x-2-2x+2=x
x-x=0
infinitely many
Escribe el nombre de algún tipo de ángulo que se forma "Entre Dos rectas Paralelas y una Secante"
Answers
Answer:
We see that opposite angles are two angles between two secant lines (“secant lines” simply means two lines that cross each other) that share a vertex (that is why they are called “vertical” angles). We see also that they are not adjacent (which means next to each other) but opposite each other.
Step-by-step explanation:
Vemos que los ángulos opuestos son dos ángulos entre dos líneas secantes (“líneas secantes” simplemente significa dos líneas que se cruzan) que comparten un vértice (por eso se llaman ángulos “verticales”). También vemos que no son adyacentes (lo que significa uno al lado del otro) sino uno frente al otro.
f
is inversely proportional to
√
g
.
When
f
=
12
,
g
=
64
Work out
f
when
g
=
16
Answers
The value of 'f' when 'g' is 16 is 24.
How to calculate the value
If 'f' is inversely proportional to square root of 'g', it can be expressed thus;
f [tex]\alpha[/tex] [tex]\frac{1}{\sqrt{g} }[/tex]
Then
f * [tex]\sqrt{g}[/tex] = constant
f₁*[tex]\sqrt{g}[/tex] ₁ = f₂ * [tex]\sqrt{g}[/tex]₂
If f₁ = 12 , [tex]\sqrt{g}[/tex]₁ = [tex]\sqrt{64}[/tex] = 8,
f₂ = ?, [tex]\sqrt{g}[/tex]₂= [tex]\sqrt{16}[/tex] = 4
Substitute into formula
12 * 8 = f₂ * 4
Make 'f₂' subject
f₂ = 96 ÷ 4
f₂ = 24
Therefore, the value of 'f' when 'g' is 16 is 24.
Learn more about indirect variations:
https://brainly.com/question/6499629
#SPJ1
Help asap please 50 points
Answers
Answer:
The area of rectangle is 8 x ² y ².
Step-by-step explanation:
Given that :- Measure of side A of rectangle is 2 xySide B measure twice the length of side A = 2 × ( 2xy ) = 4 xyTo Find :-➛ Area of rectangle
Formula Used :-➛ Area of rectangle = Length × Breadth
Solution :-Firstly we need to find Breadth of rectangle
Using Formula
Area of rectangle = Length × Breadth
Where
Length of rectangle = 2xy
Breadth of rectangle = 2 × 2xy = 4 xy
Substituting the values into the Formula
Area of rectangle = 2 xy × 4 xy
multiply, we get
Area of rectangle = 8 x² y²
Therefore, Area of rectangle is 8 x ² y ².
1 + 2 + 3 + ... + 98 + 99 + 100
Answers
Answer:
101 + 102 + 103 + ... + 998 + 999 + 1000
Step-by-step explanation:
=====================================================
Explanation:
This series is arithmetic since the common difference is 1. In other words, we're adding 1 to each term to get the next one.
The quickest way to find the sum is to use the formula below
S = (n/2)*(a+b)
where n is the number of terms, 'a' is the first term, and b is the last (or nth) term. This formula only works for arithmetic series.
We can see that n = 100, a = 1 and b = 100, so....
S = (n/2)*(a+b)
S = (100/2)*(1+100)
S = 50*101
S = 5050
-----------
This can be confirmed by noticing that we have 100/2 = 50 pairs of terms. Pair up the terms such that 1 goes with 100, 2 goes with 99, 3 goes with 98, and so on.
We have these fifty sums
1+100 = 101
2+99 = 101
3+98 = 101
....
48+53 = 101
49+52 = 101
50+51 = 101
We have 50 copies of 101 being added, which leads to 50*101 = 5050
--------------
The slowest and most tedious way to confirm this is to type 1+2+3+...+98+99+100 into your calculator. The result should say 5050. Using a spreadsheet would be a better option instead of using a handheld calculator. I don't recommend this unless you need more proof that we end up with 5050 as the final answer.
Help PLEASE 50 POINTS
Answers
Answer
I am going to answer the one thats like can you classifly each firgure
cone is the one on the far right
cylinder is the one thats a long circle kinda shape at the top
pyramid is the second to the left
prism is the one next to cylinder.
Step-by-step explanation:
Answer: Its a rectangular prisim
Step-by-step explanation: It has three dimensions, length, width, and height. Some examples of a rectangular prism in real life are rectangular tissue boxes, school notebooks, laptops, fish tanks
Christine owns 9 hair bands and additional hair bands are 2 for a dollar. How much money does she need to spend on hair bands in order to own a total of 49 hair bands?
Answers
Answer: $20
Step-by-step explanation:
If she already has 9, and she needs 49, take that extra 9 off 49 and then she needs 40 more and she gets 2 for a dollar, she'll need to spend $20 to get 40 headbands. Can I please get Brainliest?
Quadrilateral ABCD is inscribed in a circle. Angle B measures 19°. What is the measure of angle D?
Answers
Answer:
[tex]D = 161^o[/tex]
Step-by-step explanation:
Given
[tex]\angle B = 19^o[/tex]
Required
Find D
The label of the quadrilateral are not clear. However, a more complete question illustrates that B and D are opposite sides.
To solve for D, we make use of:
[tex]B + D = 180^o[/tex] ---- opposite [tex]sides[/tex] of a [tex]cyclic \\[/tex] quadrilateral
Make D the subject
[tex]D = 180^o -B[/tex]
[tex]D = 180^o -19^o[/tex]
[tex]D = 161^o[/tex]
35 points!!! Which is the general form of the equation of the circle shown?
Options shown on image.
Answers
Oscar charges $25 for the first hour of tutoring and $15 for each additional hour of fraction of an hour counting as a whole hour. the rates that Latoya charges for x hours of tutoring are modeled with with the function shown.
Choose.. will charge (5,10,15,20) more to tutor for 5.5 hours
Answers
Answer:
Latoya will charge $10 more to tutor for 5.5 hours
Step-by-step explanation:
We shall look at the total charges of both tutors individually.
Oscar charges $25 for the first hour of tutoring and $15 for each additional hour of fraction of an hour counting as a whole hour.
This means that for the first hour, Oscar charges $25.
For every subsequent hour, regardless of whether the student was tutored for the full hour or only partial, Oscar still charges $15 for the particular hour. To clarify, here is an example.
If a student is tutored for 2 hours, the cost for Oscar's tutoring is $25 (first hour) + $15 (second hour) = $40. However, if the student is still tutored for 1.5 hours, the cost for Oscar's tutoring is still $25 (first hour) + $15 (second hour) = $40. This is because Oscar counts the partial minutes as a full hour in tutoring costs.
For 5.5 hours, the cost of Oscar's tutoring is
$25 (first hour) + $15*4 (2nd to 5th hours) + $15 (the last half an hour) = $100.
Now, we shall look at Latoya's tutoring cost.
f(x) =
30x,
[tex]0 \leqslant x \leqslant 3[/tex]
20x,
[tex]3 < x \leqslant 6[/tex]
10x,
[tex]x > 6[/tex]
The tutoring cost depends on x, the number of tutoring hours. In this case, x is 5.5. The cost for 5.5 hour depends on the formula 20x since 5.5 is more than 3 but less than 6.
Hence, the tutoring cost for Latoya is $20*5.5 = $110.
In this case, Latoya charges $110-$100=$10 more to tutor for 5.5 hours.
JESSIE CAN MAKE 300 PHOTOCOPIES OF A PAGE IN 3 MINUTES. ELSA XANDO THE SAME JOB IN 6 MINUTES. IF BOTH OF THEM WORK TOGETHER, HOW LONG IT WILL TAKE THEM TO DO THE JOB?
Answers
Answer:
elsa can do 150 in 3 minutes.
so together they can do 450 in 3 minutes, or 150 in 1 minute
they would need two minutes
Answer:
4.5 minutes long to do their job.
Annabelle cuts 2 feet from a 5-foot length of rope. Then she cuts 17 inches from the rope. How many inches of rope are left?
Answers
Answer:
1.58feet
Step-by-step explanation:
Given data
Total lenght of rope= 5 feet
She cuts 2 feet
Remainder= 5-2= 3feet
Now let us convert 17inches to feet
from tables, 17inches is 1.41667feet
Hence the amount of rope now left is
=3-1.41667
=1.58feet
PLEASE HELP ME!
EXPLANATION = BRAINLIEST
the area is ___ square units
Answers
Answer:
50 units²
Step-by-step explanation:
Solve for both long sides:
6² + 8² = x²
36 + 64 = x²
100 = x²
x = 10
Solve for both short sides:
3² + 4² = x²
9 + 16 = x²
25 = x²
x = 5
Area:
5 x 10 = 50
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Step-by-step explanation:
[tex]2x^2+8x-7=-2[/tex]
Please help me with this. I know the answer for this. But the answer I got differs from the one in the answer sheet. So Please tell me what you think is the answer
Answers
Answer:
x = -2 ±√(13/2)
Step-by-step explanation:
1. Simplify by combining like terms and then evaluate for x = 2 and y=-1
a) x + 2x - 6
b) 6x – 5x-x+8y
Answers
2+2(2)-6
2+4-6
0
2. 6x-5-x+8y
6(2)-5-2+8(-1)
12-5-2-8
-27
Answer:
a)0
b)-27
Step-by-step explanation:
I simplified it u just combine the like terms
the rest should be easy
I really need help ill love you forever if you help me thank you so much
Answers
Answer:
x = 13
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
30 = 1/2 (5x-5)
Multiply each side by 2
2*30 = 2* 1/2 ( 5x-5)
60 = 5x-5
Add 5 to each side
60+5 = 5x-5+5
65 = 5x
Divide each side by 5
65/5 = 5x/5
13 = x
What is the median of the data represented in the line plot?
Answers
Answer:
The answer is Choice D
Step-by-step explanation
The median is the middle value in the given set of data.
If the data is even, then there will be two middle numbers, then the median is the average of these two middle numbers.
Thus, from the data, it is obvious that the number of data in the given set is 13.
Hence, the middle number is 23.
Therefore, the median of the data is 23.
[tex]given \: f(x) = \frac{4x - 10}{x - 2[/tex]
determine the x and y intercept of f
Answers
Given :-
f(x) = 4x - 10/ x -2To Find :-
x and y intercept .Solution :
Let ,
→ y = f(x)
So that ,
→ y = 4x - 10/ x -2
For finding x intercept , substitute y = 0 .→ 0 = 4x - 10/x - 2
→ 4x - 10 = 0
→ 4x = 10
→ x = 10/4
→ x = 5/2
→ x = 2.5
For finding y intercept , put x = 0 .→ y = 4*0 - 10 / 0 -2
→ y = -10/-2
→ y = 5
x intercept = (2.5,0)y intercept = (0,5)Need help ASAP DUE AOLN AND PLEASE SHOW WORK ?!!!
Answers
Answer: 35.98in
Step-by-step explanation:
Use the formula: h=3 v/pi(r^2)
Answer:
V = 36.0 in
Step-by-step explanation:
V of cylinder = (1/3)πr^2(h)
V of cylinder = 3052 cubic inches
r = 9 in
3052 = (1/3)π(9)^2(h)
3052 = (1/3)π(81)h
3052 = 84.82300165h
divide both sides by coefficient of h
h = 36.0 in (rounded to nearest tenth)
PLEASE PLEASE HELP ME WITH THIS PLEASE!!! ITS IXL
ANSWER EXPLANATION = BRAINLIEST
You can transform ⨀N to ⨀N' by translating it and then performing a dilation centered at N'. Find the translation rule and the scale factor of the dilation
Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.
Translation: (x,y)↦ (____, ____)
Scale factor: _____?
THANK YOU!
Answers
Answer:
ok who ever ur teacher is is kinda a mean teacher because they givin u like 98th grade questions bro i dont even know this and im in college
Step-by-step explanation:
Answer:
below
Step-by-step explanation:
The point N is at (-7, -8)
The point N’ is at (4, -4)
On the x-axis, -7 to 4 is a shift of 11 units to the right.
On the y-axis, -8 to -4 is a shift of 4 units upward.
To find the scale factor, we need to find the change in radius size.
As previously identified, the center of Circle N is (-7, -8). If we draw a vertical line from the center to the edge of the circle, the line will be 2 units long.
As previously identified, the center of Circle N’ is (-4, -4). If we draw a vertical line from the center to the edge of the circle, the line will be 6 units long.
6 is 3 times the amount of 2, meaning the scale factor is 3.
Hope this helps!
Please help me with this asap if you can.
Answers
Answer:
The first box plot is for group 2
The second box plot is for group 1
The third box plot is for group 3
is 2y=10 a function?
Answers
Answer:
2y = 10 is an equation
An equation is a statement that shows that the values of two mathematical expressions are equal (indicated by the sign =)
Which type of angle is related to supplementary angles?
Reflex
Straight
Acute
Obtuse
Answers
straight angle because the supplementary angle and straight angle is same.
How to solve this? I have no clue and also teach me on how to solve this! Thank you!!!
Answers
Answer:
90 counterclockwise or 270 clockwise
Step-by-step explanation:
just trust me bro lolskies
====================================================
Explanation:
Through some strange formatting error, the tickmarks are not in the proper locations. They should be to the right and slightly above the letter. They should be close by, and not far away like that.
It looks like the purple figure is the image while the blue figure is the preimage. If that's the case, then we've applied a 90 degree counterclockwise rotation to go from blue to purple.
Notice how angle AQA' is 90 degrees as shown by the green segments in the diagram below. So are BQB' and CQC' and DQD' as well.
We could also rotate the blue figure 270 degrees clockwise to arrive at the same purple image. Note how 90+270 = 360 which is a full circle.
Select all of the true statements.
A.
1
3
foot
>
5
inches
B.
4
miles
>
7
,
000
yards
C.
2
1
4
miles
<
10
,
000
feet
D.
5
3
4
yards
=
196
inches
E.
8
yards
=
24
feet
Answers
Answer:
miles
<
10
,
000
feet
D.
5
3
4
yards
=
196
inches
E.
8
yards
=
24
feet