Answers
Answer:
(2x,2y)
Step-by-step explanation:
Hope this helps!!!
Related Questions
differentiate the following with respect to x
irrelevant answers will be reported
Answers
Answer:
[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle y = e^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)}[/tex]
Step 2: Differentiate
Apply Derivative Rule [Product Rule]:[tex]\displaystyle y' = \big[ e^{x^2 + 7} \big]' \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = e^{x^2 + 7} (x^2 + 7)' \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Addition/Subtraction]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Trigonometric Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \cos (3x + 4) (3x + 4)' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Addition/Subtraction]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules [Basic Power Rule + Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{\big[ \csc (5x) \big] '}{2\sqrt{\csc (5x)}}[/tex]Apply Trigonometric Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{- \csc (5x) \cot (5x) (5x)'}{2\sqrt{\csc (5x)}}[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Multiplied Constant]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{-5 \csc (5x) \cot (5x)}{2\sqrt{\csc (5x)}}[/tex]Rewrite:
[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]
∴ we have found the derivative of the function.
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Learn more about differentiation: https://brainly.com/question/26836290
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
To find the derivative of the function [tex]\displaystyle\sf\:y=e^{x^{2}+7}\sin(3x+4)\sqrt{\csc(5x)}}[/tex] with respect to [tex]\displaystyle\sf x[/tex], we'll use the chain rule and product rule.
Let's break down the function into its individual parts:
[tex]\displaystyle\sf u= e^{x^{2}+7}[/tex]
[tex]\displaystyle\sf v= \sin(3x+4)[/tex]
[tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex]
Now, let's differentiate each part separately:
Using the chain rule, the derivative of [tex]\displaystyle\sf u= e^{x^{2}+7}[/tex] is:
[tex]\displaystyle\sf \dfrac{du}{dx}= (2x)e^{x^{2}+7}[/tex]
Using the chain rule, the derivative of [tex]\displaystyle\sf v= \sin(3x+4)[/tex] is:
[tex]\displaystyle\sf \dfrac{dv}{dx}= 3\cos(3x+4)[/tex]
To differentiate [tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex], we can rewrite it as [tex]\displaystyle\sf w= (\csc(5x))^{1/2}[/tex]. Using the chain rule, the derivative of [tex]\displaystyle\sf w[/tex] is:
[tex]\displaystyle\sf \dfrac{dw}{dx}= \dfrac{1}{2}(\csc(5x))^{-1/2}(-\cot(5x))(5)[/tex]
Simplifying the derivative [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:
[tex]\displaystyle\sf \dfrac{dw}{dx}= -\dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Now, using the product rule, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] can be calculated as follows:
[tex]\displaystyle\sf \dfrac{dy}{dx}= \dfrac{du}{dx} \cdot v \cdot w + u \cdot \dfrac{dv}{dx} \cdot w + u \cdot v \cdot \dfrac{dw}{dx}[/tex]
Substituting the values of [tex]\displaystyle\sf \dfrac{du}{dx}[/tex], [tex]\displaystyle\sf \dfrac{dv}{dx}[/tex], and [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:
[tex]\displaystyle\sf \dfrac{dy}{dx}= \left((2x)e^{x^{2}+7}\right) \cdot \sin(3x+4) \cdot \sqrt{\csc(5x)} + e^{x^{2}+7} \cdot \left(3\cos(3x+4)\right) \cdot \sqrt{\csc(5x)} - e^{x^{2}+7} \cdot \sin(3x+4) \cdot \dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Simplifying further:
[tex]\displaystyle\sf \dfrac{dy}{dx}= \left(2xe^{x^{2}+7}\right) \sin(3x+4) \sqrt{\csc(5x)} + 3e^{x^{2}+7}\cos(3x+4) \sqrt{\csc(5x)} - \dfrac{5e^{x^{2}+7} \sin(3x+4) \cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:
[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 3e^{x^{2}+7}\sqrt{\csc(5x)}\cos(3x+4) - \dfrac{5e^{x^{2}+7}\sin(3x+4)\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Simplifying further, we have:
[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x \sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]
Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:
[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
ethan puts 1/3 pound of dog food into dog bowls every time he fills it. How many times can ethan fill his dog's bowl with 5 pounds of dog food?
Answers
Answer: Ethan can fill the bowl(s) 15 times.
Step-by-step explanation:
Identify the initial amount in the following exponential function: y = 2.3(1.32)
Answers
The perimeter of a notebook is 28
inches. The area is 48 square inches.
What are the dimensions of the
notebook?
Answers
Area = length x width
Half the perimeter = length + width
half the perimeter = 14 inches.
Find 2 numbers when added together = 14 and when multiplied together = 48
6 + 8 = 14
6 x 8 = 48
the dimensions are 6 inches by 8 inches
Which is an equivalent fraction for
?
A
12\frac{1}{2}
2
1
B
26\frac{2}{6}
6
2
C
46\frac{4}{6}
6
4
D
32\frac{3}{2}
2
3
Answers
Answer:
I believe the answer is C
Step-by-step explanation:
If the half-life of that substance is 22 days, and only 1/4 of it remains, how many days have elapsed?
A- 11 days
B-22 days
C-44 days
D-88 days
Answers
Answer:
11
Step-by-step explanation:
if half of it is 22, then a whole life is 44 days. 1/4 of 44 days is 11 days so its A
Answer:
the answer is A (11 days)
Step-by-step explanation:
Hope this helps you!
A textile factory uses a 43 pound bucket of dye to color a roll of fabric that is
1,067 feet long. if the company has 4 buckets of dye, can it color 5 rolls of
fabric?
Answers
Answer:
No
Step-by-step explanation:
At one bucket per roll, four buckets will color four rolls, not 5.
__
The company cannot color 5 rolls of fabric with 4 buckets of dye.
What time is it on the clock?
Answers
Answer:
About 2:18
The minute hand points toward the [tex]\frac{1}{4}[/tex] marker, meaning that is 15 minutes.Count the other ticks, and that's 18.Since the hand is not exactly on the 3, that means it is 2:00With this information, we can make a hypothesis or come to a conclusion that the clock says 2:18
what is the measure of the angle shown?
Answers
Answer:
35 degrees
Step-by-step explanation:
Answer:
The measure of the angle is 35 degrees
Step-by-step explanation:
There are two measurements on the protractor.
If the angle is acute you will use the smaller measurenment of the two, and if the angle is obtuse, you will use the larger of the two.
In this case the angle is acute, so the measure is 35 degrees.
Hope that helps!
Without solving the addition problems, tell whether the answers are going to be odd or even. Model 39 +42 odd 1. 64 + 82 2. 129 + 377 3. 468 +599 4. 1,987 + 9,888 Activity 4 Without solving the multiplication problems, tell whether the answers are going to be odd or even. Model 39x42 even 2. 137 x 141 1. 78 X 44 4. 5,111 x 8,222 3. 528 X 603.
SOS HOMEWORK
Answers
Answer:
3. 1067
4. 11875
5. 1638
6. 19317
7. 3432
8. 42022642
9. 318384
An eight-sided dice is rolled twice. The numbers are 1 through 8. What
is the probability that it will land on the number 7 twice in a row?
Answers
Answer:
1/64
Step-by-step explanation:
The probability of both dice being a 1 is 1/8 * 1/8 = 1/64
A researcher is studying the relationship between the number of TVs owned by a family and the size of the family's electric bill. After collecting data, he finds that the relationship is best modeled by the equation B = 2.43T + 95.66, where B is one month's electric bill in dollars and T is the number of TVs owned by the family. Which of these is a good interpretation of the y-intercept of this model?
Answers
Answer:
Step-by-step explanation:
No choice is given but here is the general interpretation.
Y-intercept is where the plot crosses the y-axia at x=0. In this case, x is T which represents number of TVs owned by the family. T=0 meaning there is no TV and B = 96.66 is the one month's electric bill in dollars for all other appliances in the home.
Given function
B=2.43T+95.66Now
Compare to slope intercept form y=mx+b
Slope=m=2.43Y intercept=b=95.66Here y intercept may be the fixed charge .
Write a numerical expression to represent the phrase.
the difference of 4 cubed and 25
Answers
Hello!
First, "the difference" of 2 numbers means you subtract these numbers.
Then, 4 cubed is written as follows:
4³
Subtract:
4³-25
[If necessary] Evaluate:
64-25
39
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
HELP PLEASE!! 20 Points!! Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
Answers
Answer:
my answer was wrong
given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 24 nd DC = 12, what is the length of AD?
Answers
Answer:
Step-by-step explanation:
YES IS THE ANSWER BECAUSE X=9
AND 11+3=87
After measuring the heights of 7 people, they have an average height of 156cm. after
measuring the heights of 8 people they have an average height of 158cm. how tall is
the 8th person?
Answers
Answer:
8th Person = 172 cm tall
Step-by-step explanation:
( a + b + c + d + e + f + g )/7 = 156
a + b + c + d + e + f + g = 1092 total size
----------------------------------------------------------
now they measured 8 people (a + b... g) + h, but we know the total size of the other 7 = 1092
a + b + c + d + e + f + g + h
( 1092 + h )/8 = 158
1092 + h = 158*8
h = 1264 - 1092
h = 172
-----------------------------------
the 8th person is 172 cm tall
Manny has 36 coins in
his piggybank.
3 of the coins are silver dollars.
• The remaining coins are dimes (10€), quarters (25€) and nickels (5¢).
• There is an equal number of dimes, quarters and nickels.
How many nickels does Manny have?
Answers
Answer:
q=50
d=22
Step-by-step explanation:
Can anyone help me with this one Question on volume The diameter of a cylinder is 1 yd. The height is 12 yd. Find the volume of the cylinder.
Answers
Answer:
9.42 cube.yd
Step-by-step explanation:
Volume of cylinder= πr^2h
3.14 × 0.5 × 0.5 × 129.42 cube.ydUse the example above and determine the fraction of total interest owed. After the fourth month of a 12 month loan, the numerator is: {(n + ) + (nt ) + (n + ) + (n + and the denominator is: {(n) + (n + 1) + ... + (n + )} Therefore, the fraction is numerator/denominator (to the nearest tenth) = %.
Answers
Answer:
Step-by-step explanation:
The picture does not show the example which will help in determining whether it is simple or compound interest calculation.
Based on what is shown, the answer is:
the numerator is: {(n + 11) + (n + 10) + (n + 9 ) + (n + 8) = 4n + 38;
and the denominator is: {(n) + (n + 1) + ... + (n + 11) = 12n + 66.
Therefore, the fraction is numerator/denominator:
= (4n + 38) / (12n + 66)
In this case n=1, the fraction = 42/78 = 0.53846
= 53.85%
Which geometric figure would be the best to model a suitcase?
Answers
Answer:
A rectangular prism would be best to model a suitcase
Step-by-step explanation:
Hope that helps!
Answer:
Rectangular Prism
Step-by-step explanation:
If you look at a suitcase, it resembles a rectangular prism quite well.
which expression is equavilent to the epression -3(4x - 2) - 2x?
A. -8x
B. -16
C. -14 - 2
D. -14 + 6
Answers
Answer:
D
Step-by-step explanation:
-3(4x - 2) - 2x
-12x + 6 -2x
-14x + 6
Will choose Brainliest.
Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.
How many more cookies will Jessica have than Martha?
If x represents the number of cookies Jessica started with, complete the statements below.
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0
Jessica has at least
_ cookies more than Martha.
Answers
That part is total cookies as per algebraic formula x^2-(a+b)x+ab=0
Hence
The inequality is
[tex]\\ \rm\rightarrowtail x^2-30x+224>=0[/tex]
[tex]\\ \rm\rightarrowtail (x-14)(x-16)>=0[/tex]
[tex]\\ \rm\rightarrowtail 14\leqslant x\leqslant 16[/tex]
Solution range
[14,16]Atleast means the range
16-142Atleast 2 more than Martha
Solve for x.
32
(2x - 12)°
Answers:
x = 35
X= 51
x = 80
x = 96
Answers
If VZ=p–7 and WY=p–21, what is the value of p?
Answers
Answer:
p = 35
Step-by-step explanation:
the midsegment WY is half the measure of VZ , that is
WY = [tex]\frac{1}{2}[/tex] VZ ( substitute values )
p - 21 = [tex]\frac{1}{2}[/tex] (p - 7) ← multiply through by 2 to clear the fraction
2p - 42 = p - 7 ( subtract p from both sides )
p - 42 = - 7 ( add 42 to both sides )
p = 35
A function f is defined by f(x, y) = 3x2 – 4y. What is the value of
f(3, 2)?
Answers
Assuming the function is [tex]f(x,y)=3x^2-4y[/tex]
--> then f(3,2) is: [tex]f(3,2) = 3(3^2)-4(2)=3*9-8=27-8=19[/tex]
Hope that helps!
I will give BRAINILEST
Answers
Answer:
The players club is playing with the players
Step-by-step explanation:
give me a good Answer to my Question
What is the scale factor of this dilation? a:1/2 b:2/3 c:3/4 d:3/2
Angle FGH is a right angle.
The measure of angle JGH is 50.
The measure of angle FGJ is
What is the value of x?
Answers
Answer:
since its a triangle then angles have to be 90 (the right angle) and 50 (which is given)
180-90-50 = 40
Answer = 40
Step-by-step explanation:
this question is too hard
Answers
Answer:
27 children
Step-by-step explanation:
For every 9 children, there are 4 adults. Those numbers added together equal 13. Now, if we divide the total number of adults and children by 13, we will get the number of how many groups there are of 9 kids and 4 adults.
39 / 13 = 3
There are 3 groups of 9 kids and 4 adults, which means to find the total number of children, we have to multiply 3 by 9.
3 * 9 = 27
Therefore, there are 27 children total. I know this was probably really confusing, but I hope it helped in some way! Have a lovely day!! :)
Look at these equations.
9 = 7+ a
a + 8 = b + 5
Use both equations to work out the value of B
Answers
Answer:
B=5
Step-by-step explanation:
If 7 plus a equals 9 then a would equal 2.
2+8=b+5
10=b+5
Ask yourself what number plus 5 equals 10
B is 5 because 5 plus 5 is 10
1 2/3x=1/2
what is x?
x/2.5=1.75
what is x?
Answers
Answer:
Step-by-step explanation:
1. 12/3x = 1/2
4/1x = 1/2
4/1x = 1/2 / 4/1
1/2 x 1/4 , x = 1/8.
2). x / 2.5 = 1. 75/ 1
cross multiply to get
x = 2.5 x 1.75
x = 4.375