We are given with a function y and need to find dy/dx or the first Derivative of y w.r.t.x , but let's recall
[tex]{\boxed{\bf{\dfrac{d}{dx}\{f(x)\pm g(x)\pm h(x)\pm \cdots =\dfrac{d}{dx}\{f(x)\}\pm \dfrac{d}{dx}\{g(x)\}\pm \dfrac{d}{dx}\{h(x)\}\pm \cdots}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}(log_{e}x)=\dfrac{1}{x}}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}(e^x)=e^{x}}}}[/tex]Now consider :
[tex]{:\implies \quad \sf y=e^{x}-\dfrac{1}{x}+log_{e}x}[/tex]
Differentiating both sides w.r.t.x
[tex]{:\implies \quad \sf \dfrac{d}{dx}(y)=\dfrac{d}{dx}\bigg\{e^{x}-\dfrac{1}{x}+log_{e}x\bigg\}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=\dfrac{d}{dx}(e^x)-\dfrac{d}{dx}\left(\dfrac{1}{x}\right)+\dfrac{d}{dx}(log_{e}x)}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}-\dfrac{d}{dx}(x^{-1})+\dfrac{1}{x}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}-(-1)(x)^{-1-1}+\dfrac{1}{x}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}+(x)^{-2}+\dfrac{1}{x}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}+\dfrac{1}{x^{2}}+\dfrac{1}{x}}[/tex]
Simplifying will yield
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\dfrac{dy}{dx}=\dfrac{e^{x}x^{2}+x^{2}+x}{x^{2}}}}}[/tex]
This is the required answer
Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
The equation of the line passing through the point (-1, 1) and (0, 10) is y = 9x + 10
What is a linear function?A linear function is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the y intercept.
From the table, using the point (-1, 1) and (0, 10) ,hence:
[tex]y-1=\frac{10-1}{0-(-1)} (x-(-1))\\\\y=9x+10[/tex]
The equation of the line passing through the point (-1, 1) and (0, 10) is y = 9x + 10
Find out more on linear function at: https://brainly.com/question/15602982
Andrew expected 60 for his birthday but only got 40 what is the percent of error
= 20/60 x 100 = 33.3
Find the measures of the interior angles of the triangle. Find A, B, C
Answer:
Step-by-step explanation:
Someone please help me quick! And no link please
Answer:
m∠TSR = 68°
explanation:
As its an isosceles triangle. We can determine that m∠TSR = m∠TRS
The total interior angles inside the triangle sum up to 180°
solve:
x + x + 44° = 180°2x = 180° - 44°2x = 136°x = 68°
The narrators of “Excerpt from Bloomability” and “Excerpt from Secrets of the Cicada Summer” face
similar problems. What problems do the narrators face? How are these problems similar, and how are
I they different? Use details from both stories to support your response.
DDDD
In your response, be sure to:
• explain the problem the narrator faces in the “Excerpt from Bloomability"
explain the problem the narrator faces in the “Excerpt from Secrets of the Cicada Summer"
describe how the problems are similar and how they are different
use details from both stories to support your response
file Cicada Smey have
In these texts, the narrators have problems with their identity as they feel invisible and do not feel they are different from other people. However, while n the "Secrets of the Cicada Summer" the author only sees herself as invisible, in "Bloomability" the author is wondering if she wants to be invisible.
What is the problem in "Bloomability"?In this story, the narrator is indecisive about her personality and traits because she wonders whether she wants to be like everybody or she wants to be different. Also, it seems the narrator still does not know herself or what she wants to do in her life as she mentions "Waiting to see who I was and what sort of life I might lead".
What is the problem in "Secrets of the Cicada Summer"?In this text, the narrator feels invisible and lonely. This idea is shown in excerpts such as "He doesn't notice me because I'm invisible".
What are the similarities and differences?Both texts refer to themes such as solitude and invisibility.The attitude of the narrators is different, in the first text the narrator wonders if it is better to be invisible or not, but in the second one, the narrator defines herself as invisible.Learn more about narrator in: https://brainly.com/question/2053270
The quadrilateral is a rhombus. What is QT?
Step-by-step explanation:
qu = 5y - 4
and qt is half of qu
so
qt = [tex]\frac{5y - 4}{2}[/tex]
Answer:
QT = 8
Step-by-step explanation:
the sides of a rhombus are congruent , then
PS = RS ( substitute values )
3y - 1 = 2y + 3 ( subtract 2y from both sides )
y - 1 = 3 ( add 1 to both sides )
y = 4
The diagonals of a rhombus bisect each other
QS = 5y - 4 = 5(4) - 4 = 20 - 4 = 16
then
QT = [tex]\frac{1}{2}[/tex] QS = [tex]\frac{1}{2}[/tex] × 16 = 8
Write these fractions with the same denominatior 3/5= 2/3=
30
Explanation:
5×6=30
3×10=30
hope this helps...I just looked it up and this is what I found
Answer:
you multiple 5 with 3 and 3 with 5
3×5=15
5×3=15
that will give
3/15= 2/15
What is the range of f(x) = ( 3/4)* - 4?
{yly>-4}
{yly> 3/4}
{yly<-4}
{yly< 3/4}
Answer:
the answer is {y | y> - 4}
John wants to buy a new phone which costs$1000. 0. He has $175. 00 in his piggyback. He works in a grocery store down the street for $12. 50 an hour. How many hours will he need to work before he can buy his new phone ?
Answer:
66 hours
Step-by-step explanation:
1. 1000 - 175 = 825
(He needs $825 left.)
2. 825/12.50=66
He needs to work 66 more hours before he can buy his new phone.
Each graph below shows a relationship between x andy .
For each graph, determine whether x and y are proportional.
If x and y are proportional, fill in the blank with a number.
Answer:
graph 1 but im not sure check with someone else.
Step-by-step explanation:
if you divide 10 divided by 2 it gives you 5 and then subtract it by 2.2 = 2.8
there goes your answer.
Answer Each graph below shows a relationship between x and y. For each graph, determine whether x and y are proportional. If x and y are proportional, fill in the blank with a number in simplest form:
Step-by-step explanation:
Someone pls help????????????????????????
Answer:
226 with r=295
Step-by-step explanation:
when you use long division, you get a final answer equaling 226, however, your left with a r/remainder of 295.
hope that helps
if it does, please give me brainliest.
thanks so much!
if the figure is translated 4 until s left, what are the coordinates
Answer:
C, (-4, 0)
Step-by-step explanation:
Hope this helps you. Have a good day. :)
Identify the type of the pairs of angles.
∠3 and ∠5
∠1 and ∠8
∠2 and ∠6
∠1 and ∠4
∠4 and ∠5
write the ratio of the first measurement to the second measurement. compare in millimeters. diameter of ball A: 48mm diameter of ball B: 6.8cm
Answer:
A is the Answer
Step-by-step explanation:
A is the correct answer
HELP ASAP PLEASE ILL MAKE BRAINLIEST
Answer:
The answer is 49 inches
Step-by-step explanation:
Divide 294 by 6 to get the answer.
Hope that helps!
Answer:
49 inches
We know that for every 6 feet in real life, there will be 1 inch in the picture.
So, that means if we divide 294 by 6, we can find how many inches wide the picture is.
294 ÷ 6 = 49
Since there are 49 sixes in 294, the picture is 49 inches wide.
18+6/-4-16 HELP only d part
Answer:
[tex]\frac{1}{2}[/tex] is the answer
Step-by-step explanation:
First we need to substitute X and Y with their respective numbers
[tex]3\cdot \:6+\frac{6}{-4}-\left(-4\right)^2[/tex]
Then, following PEMDAS, We just need to simplify
[tex]18+\frac{6}{-4} -16[/tex]
[tex]16.5-16=0.5=\frac{1}{2}[/tex]
find x please image below
Answer:
x=54°
...
...
.....
....
Which geometric series represents 0.4444... as a fraction? one-fourth startfraction 1 over 40 endfraction startfraction 1 over 400 endfraction startfraction 1 over 4,000 endfraction ellipsis startfraction 1 over 40 endfraction startfraction 1 over 400 endfraction startfraction 1 over 4,000 endfraction startfraction 1 over 40,000 endfraction ellipsis four-tenths startfraction 4 over 100 endfraction startfraction 4 over 1,000 endfraction startfraction 4 over 10,000 endfraction ellipsis one-tenth startfraction 1 over 100 endfraction startfraction 1 over 1,000 endfraction startfraction 1 over 10,000 endfraction ellipsis
The geometric series which represent the provided number in the fraction form is,
[tex]\dfrac{4}{10}, \dfrac{4}{100},\dfrac{4}{1000},\dfrac{4}{10,000}[/tex]
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
The fraction number given in the problem is,
[tex]n=0.4444.....[/tex]
Let's break the given number into the parts as,
[tex]n=0.4+0.04+0.004+0.0004+.....[/tex]
The decimal number 0.4 is written as 4/10. Similarly, 0.04 can be written as 4/100. Thus, the above number can also be written as,
[tex]n=\dfrac{4}{10}+\dfrac{4}{100}+\dfrac{4}{1000}+\dfrac{4}{10,000}+\cdots[/tex]
Hence, the geometric series which represent the provided number in the fraction form is,
[tex]\dfrac{4}{10}, \dfrac{4}{100},\dfrac{4}{1000},\dfrac{4}{10,000}[/tex]
Learn more about the geometric sequence here;
https://brainly.com/question/1509142
Answer:
it b
Step-by-step explanation:just did the quiz
An apple, potato, and onion all taste the same if you eat them with your nose plugged
Is this true?
No
Because they all are different in taste and smell
True!
Explanation: Apples, potatoes and onions will all taste the same if somehow you were to block your sense of smell (plug your nose).
HELPPPP
F(x)=-x^2-3x+1
The quadratic function, f(x )or g(x) has the greater maximum value ??
Answer:
You can tell that the maximum value that attains is rough.
Rewriting in vertex form. This tells us that the maximum of is.
So has the greater maximum.
Step-by-step explanation:
Please answer as soon as possible will give brainliest.
Answer: -12x^2 + 4x
Step-by-step explanation:
Really need help on this
A buyer and seller agree that 4 blocks of salt weigh the same as 1 gold bar if this is true how many gold bars would weigh the same as 21 blocks of salt
Answer:
5.25 gold bars are needed to get it to weigh the same as 21 gold bars.
Step-by-step explanation:
ratio = 4 blocks of salt : 1 gold bar
to get the amount of gold bars needed to weight the same amount as 21 blocks of salt divide 21 by 4
21 ÷ 4 = 5.25
21 blocks of salt : 5.25 gold bars
5.25 gold bars are needed to get it to weigh the same as 21 gold bars.
I don't know if this is what you're looking for but I hope it helps.
I NEED HELP GIVING BRAINLIEST
Answer:
For 1) you must do that yourself from least to greatest.
2) most snow was 3 and 3/4
3) least snow was 1 and 2/4
4) it snowed 3 and 1/4 3 days long.
5) it could have been 4 and 2/4 with another 1 and 2/4 since that makes three or maybe just 4 with 1 since that also makes three there are a lot of possibilities considering it only has to be subtracted and equal three.
Step-by-step explanation:
Hope this helped.
A brainliest is always appreciated.
A water park sold 528 child tickets and 297 adult tickets. What percentage of the tickets sold were child tickets?
Answer:
64%
Step-by-step explanation:
Two thirds of a number decreased by the product of a number and two, squared, is 43
Answer:
Answer is 49
Step-by-step explanation:
Which of these is a point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7)
Answer: y-7=-0.25(x+3)
Step-by-step explanation:
Answer correctly please asap!!
Below are the results of tossing a number cube 10 times. Find the experimental probability of tossing 4.
2 6 3 5 4 4 1 2 4 3
a. 2/5
b. 3/10
c. 1/5
d. 1/6
Please answer this question I need to answer please answer HURRY!!!!
Answer:
52
Step-by-step explanation:
[tex]r^{2} -14+8p[/tex]
Substitute values given:
[tex](8)^{2} -14+8(\frac{1}{4} )[/tex]
Simplify:
64-14+2
50+2
52
Therefore 52 is our answer
Answer:
56
Step-by-step explanation:
if r = 8 than r to the second power is 8 to the second power (or 8x8) which equals 64
64 - 14 + 8p
If p + 1/4 = 2
64 - 14 + 2
54 + 2
56
I will mark brainliest! Please help
Answer:
2 seconds
Step-by-step explanation:
This means the height, and thus h(t), is equal to zero.
0=-16t^2 + 16t + 32
0= t^2 - t - 2 (divide both sides by -16)
0 = (t-2)(t+1) [factor]
t = -1, 2 [set each factor equal to zero]
But as time cannot negative, take t=2, giving us 2 seconds.