How do you differentiate y=x^(e^x) ?

How Do You Differentiate Y=x^(e^x) ?

Answers

Answer 1

We are given the function to differentiate:

[tex]{\quad \qquad \sf \rightarrow y=x^{e^x}}[/tex]

Do take natural log on both sides, then we will be having

[tex]{:\implies \quad \sf ln(y)=ln(x^{e^{x}})}[/tex]

[tex]{:\implies \quad \sf ln(y)=e^{x}ln(x)\quad \qquad \{\because ln(a^b)=bln(a)\}}[/tex]

Now, differentiate both sides by using so called chain rule and the product rule

[tex]{:\implies \quad \sf \dfrac{1}{y}\dfrac{dy}{dx}=e^{x}ln(x)+\dfrac{e^x}{x}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\dfrac{dy}{dx}=x^{e^x}\bigg\{\dfrac{e^x}{x}+ln(x)e^{x}\bigg\}}}}[/tex]

Hence, Option B) is correct

Product rule of differentiation:

[tex]{\boxed{\bf{\dfrac{d}{dx}(uv)=u\dfrac{dv}{dx}+v\dfrac{du}{dx}}}}[/tex]

Where, u and v are functions of x


Related Questions

Find a radius of a circle the length of which is 24π cm.

Answers

Answer:

12

Step-by-step explanation:

Length of a circle = circumference = 2πr = 24π

                                            Radius (r) = 24π/2π

                                                             = 12cm

3/5x2/5x4/9 in simplest form

Answers

Answer:

8/75 is the answers for the question

what is the rule for the numbers 1; 2; 4; 7; 11; 16​

Answers

Answer:

n²+n+2

Step-by-step explanation:

1)Find the difference between the numbers.

Difference= +1,+2,+3,+4,+5

2)Find the second difference between the first differences.

Difference= +1 each time

2 differences=Quadratic sequence

3)Quadratic Sequence Equation= an²+bn+c

Find the values of a, b and c by using these terms:

a (bottom)

2a+b (middle)

a+b+c (top)

4)Substitute values into equation

a=1    b=1    c=2

n²+n+2

Simplify 5^3/5^7 leaving your anwser in index form help!!!!!!!!

Answers

Answer:

0.0016

Step-by-step explanation:

Hope this helps!

A 45-foot tall tree is leaning towards a house, making an 86° angle with the ground. To stop the tree from leaning further, a cable is tied from the top of he tree and secured to a point on the ground 30 feet from the tree, opposite from the house. What angle does the cable make with the ground?​

Answers

The angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.

What is law of cosine?

Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]

(c is opposite side to angle A)

Consider the diagram attached below.

In the diagram given, we have:

AB = tree with length of 45 ft

AC = cable, with length of 'x' ft (assume)

BC = distance of the base of the cable from the base of the tree of measurement 30 ft.

AD = vertical height of the point A (the top of the tree and cable) from the ground of 'h ft' (assume),

Using the cosine rule for the triangle ABC, taking:

|AC| = x = length of the side opposite to the known angle

|AB| = 45 ft and BC = 30 ft are rest of the two sides,

Angle opposite to AC is of 86°

Thus, we get:

[tex]45^2 + 30^2 -2(30)(45)\cos(86^\circ) = x^2\\\\2925 - 188.34 \approx x^2\\\\x \approx \sqrt{2736.66} \approx 52.31 \: \rm ft[/tex]

(took positive root because of x being length, which is a non-negative quantity).

For triangle ABD, using the sine ratio from the perspective of angle A, we get:
[tex]\sin(m\angle A) = \dfrac{\text{side opposite to A}}{\text{length of hypotenuse}} \\\\\sin(86^\circ) = \dfrac{h}{45}\\\\h = \sin(86^\circ) \times 45 \approx 44.89 \: \rm ft[/tex]

Now, for the triangle ACD, using the sine ratio from the perspective of angle C (smaller than 90°), we get:

[tex]\sin(m\angle C) = \dfrac{\text{side opposite to C}}{\text{length of hypotenuse}} \\\\\sin(\theta^\circ) = \dfrac{h}{x} \approx \dfrac{44.89}{52.31} \approx 0.858\\\\\theta =\sin^{-1}(0.858) \approx 59.09, 120.90[/tex]

Taking the angle smaller than 90°, we get:

[tex]\theta \approx 59.09^\circ \approx 59^\circ[/tex]


Thus, the angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.

Learn more about law of cosines here:

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Answer:

That wasn't the correct answer

Step-by-step explanation:

c^2=45^2+30^2 - 2(45)(30)*Cos(94

c^2=2925+188.3425

c^2=3113.3425

take the square root:

c is approx. 55.8

sin86/55.8=sinx/45

55.8sinx=45sin94

divide both sides by 55.8

sinx=0.8045

sin^-1(0.8045)=53.6

Answer is 53.6 or "L" on the scavenger hunt worksheet

Phone numbers consist of a three-digit area code followed by seven digits. if the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? how did you come up with your answer? a. 8 times 10 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 6,400,000,000 b. 8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000 c. 8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 = 128,000,000 d. 8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 times 10 = 12,800,000,000

Answers

The possible number of different phone numbers will be 128000000

What is probabilty?

The extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.

In this exercise we have to use the knowledge of probability to find the phone number, so:

1 280 000 000 different ways.

First we have to establish some information about this exercise such as:

The first slot cannot start with 0 or 1, which leaves us 2, 3, 4 ..., 9 to fill.This means we have 8 different arrangements for the first slot.The second slot have a 0 or 1 for the second digit, which leaves us with 2 different arrangements.There are no restrictions for the third slot, so we would have 10 different arrangements.

Thus, now calculating the possibilities of occurrence, we have:

[tex]8\times 2\times 10=160[/tex]

[tex]8\times 10^6=8000000[/tex]

[tex]160\times 8000000=1280000000[/tex]

See more about probability follow

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show work and do it fast

Answers

Answer:

9 x 2/8 = 9/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

9 divided by 2/8 but make the 2/8 into a decimal and the turn back to a fraction if it ask if not then leave it how it is and if you have to round which you prolly wont have to but ask to make sure ight

The value of a car is $25,500. It loses 14% of its value every year.

Answers

The car value is $25,500. If it depreciates 14% (0.14) every year it would lose $3,500 every year

25,000*0.14= 3500

Y=

What is the value of x in the matrix equation below?

Answers

Answer:

-3

Step-by-step explanation:

Which rigid transformation(s) can map triangleabc onto trianglefed? reflection, then dilation reflection, then translation rotation, then translation rotation, then reflection

Answers

Answer:

rotation

Step-by-step explanation:

reflection

Answer:

rotation then translations-- C

Step-by-step explanation:

yes. and bc taking the quiz rn

What is the volume of the rectangular prism shown below?



A. 224 in³
B. 320 in³
C. 512 in³
D. 5,120 in³

Answers

Answer:

[tex]\boxed{\sf{5120\ in^3}}[/tex]

Step-by-step explanation:

Solution:

Volume of the rectangular prism formula:

[tex]: \Longrightarrow \sf{V=l*w*h}[/tex]

Given:

Length: 32 inWidth: 10 inHeight: 16 in

Then, you multiply.

[tex]\sf{32*10*16=\boxed{\sf{5120}}[/tex]

Therefore, the correct answer is "D. 5120 in³".

Answer:

D

Step-by-step explanation:

Help immediate!! Find the value of
x
xx in the triangle shown below.
x
=
x=x, equals




degrees

Answers

180-(97+47)=36°
x = 36°

B1 of a trapezoid in which Area = (48x+68) inch squared, Height = 8 in, B2 = (9x + 12) in.

what I have so far is

48x +68 = 8 (B1 + 9x +12)

what do I do from there????????????????? the question is asking to solve for Base 1/ B1

Answers

A=(1/2)(b1+b2)h =

=(48x+68)in² = (1/2)( b1+(9x+12))8

=b1= 3x+5

What is the range of possible sizes for side xxx?

Answers

Answer:

2.3<x<8.7

Step-by-step explanation:

find the height and area of the equilateral triangle ​

Answers

As here we are given with an equilateral triangle, whose side is 3 cm, and we need to find the height and area of the equilateral triangle. So, for this let's recall that, the area of any equilateral triangle with side a is given by ;

[tex]{\boxed{\bf{Area_{(Equilateral\:\: Triangle)}=\dfrac{\sqrt{3}}{4}a^{2}}}}[/tex]

So, if we substitute a = 3, in our Formula, it will yield to

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(3)^{2}}[/tex]

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(9)}[/tex]

[tex]{:\implies \quad \boxed{\bf{Area_{(Equilateral\:\:Triangle)}=\dfrac{9\sqrt{3}}{4}\:\:cm^{2}}}}[/tex]

Now, as we know that, for any triangle we also have a formula that is ;

[tex]{\boxed{\bf{Area_{(Triangle)}=\dfrac{1}{2}\times Base\times Height}}}[/tex]

Now, Here as the triangle is equilateral, so it's base will just be same 3, and if we let height be H, so we will be having

[tex]{:\implies \quad \sf \dfrac{1}{2}\times 3\times H=\dfrac{9\sqrt{3}}{4}}[/tex]

[tex]{:\implies \quad \sf H=\dfrac{9\sqrt{3}}{4}\times \dfrac23}[/tex]

[tex]{:\implies \quad \boxed{\bf{Height=\dfrac{3\sqrt{3}}{2}\:\:cm}}}[/tex]

Help me find the perimeter of the shape please!

Answers

Answer: 10m +27

Step-by-step explanation: Add all the sides together to calculate Perimeter.

2(2m +10)+2m+7+2m +2m

4m + 20 + 2m +7 +2m +2m

10m +27

2. 3x = 18 then the value of x is

Answers

Answer:

x=6

Step-by-step explanation:

(I don't know if you mean question 2 3x= 18 or 2 times 3x = 18)

2.3x = 18
3x = 18 / 2 = 9
x = 9/3 = 3

Or : x = 18/3 = 6

m∠A=(y−16)° plese help me i really need this answer

Answers

I don't know what u r trying to find out so pls tell me what u r trying to find out.

But if u r trying to find out y here,

It is impossible to find out value of y, as we don't have the value of a or any other hints which will help in finding y.

But we can write the equation in a different way,

that is...

A - y = - 16°

Solve : 4-3sec²A = 0​

Answers

Answer:

[tex]\sf\:Negative = \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\\\sf\: Positive = \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

Step-by-step explanation:

[tex]4 - 3 \sec ^ { 2 } \theta = 0[/tex]

Let's solve this.

Isolate sec²θ.

[tex]4 -3 \sec ^ { 2 } \theta = 0\\- 3 \sec^{2}\theta = -4\\3 \sec^{2}\theta=0\\\sec^{2} \theta=\frac{4}{3}[/tex]

Now, we now that, cos θ is the reciprocal of sec θ. Therefore,

[tex]\sec^{2}\theta = \frac{4}{3}\\\cos^{2}\theta = \frac{3}{4}[/tex]

Bring the square root on both the sides of the equation to remove the square.

[tex]\sqrt{\cos^{2}\theta} = \sqrt{\frac{3}{4} }\\\cos^{2}\theta = (+/-) \frac{\sqrt{3} }{2}[/tex]

If,

[tex]\cos\theta = + \frac{\sqrt{3}}{2}\\= cos \left( \frac{\pi}{6} \right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

Also if,

[tex]\cos\theta = -\frac{\sqrt{3}}{2}\\= \cos \left(\pi - \frac{\pi}{6}\right)\\= \cos \left({\frac{5\:\pi}{6}\right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Solving quadratic equations using the quadratic formula.

Answers

Answer:

what is there supposed to be a picture

Answer:

Down Here ↓↓↓

Step-by-step explanation:

Hello!

Standard Form of a Quadratic: [tex]ax^2 + bx +c[/tex]

Quadratic Formula: [tex]x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

To solve a quadratic using the quadratic formula, you have to plug values in for "a", "b", and "c" into the quadratic equation. Let's go over an example question.

Question: [tex]2x^2 +4x+2[/tex]

Solution:

Determine the values of "a", "b", and "c".

a = 2b = 4c = 2

Plug it into the quadratic equation to solve.

Solve:

[tex]x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex][tex]x = \frac{-(4) \pm\sqrt{(4)^2-4(2)(2)}}{2(2)}[/tex][tex]x = \frac{-4 \pm\sqrt{16 - 16}}{4}[/tex][tex]x = \frac{-4 \pm\sqrt{0}}{4}[/tex][tex]x = \frac{-4}{4}[/tex][tex]x = -1[/tex]

The value of x is -1.

Which algebraic expression is equivalent to the expression below? 12(5 + 3x) + 18
A.
36x - 78
B.
3x + 78
C.
36x + 78
D.
36x + 42

Answers

Step-by-step explanation:

12(5 + 3x) + 18

60+36x+18

C)36x+78

Ariana is playing a game. For each of her turns, she rolls a number cube landed with the numbers 1 through 6. She also spins the spinner shown below. To win the game Ariana needs to roll a 3 and spin a 3 on her next turn. What is thr probability that Ariana will win the game on her next turn?

Answers

Answer:

1/18

Step-by-step explanation:

probability of getting a three= 1/6

probability of getting a three on a wheel=1/3

probability of winning= 1/6x1/3=1/18

A racerunner is 26. 7 cm long. How much less than a meter is this?

Answers

Answer:

73.3 cm

Step-by-step explanation:

please helppppppppppppppp!!!!!!!!!!!!!!!!!!!!!11

Answers

The anwser is sympathetic and geographical

pls help
Is this triangle acute, right or obtuse?

Answers

Probably between obtuse angle or triangle because sometimes they trick you

But I'm not 100 percent sure

Answer:

It is right

Step-by-step explanation:

Right triangles will always form a corner like an L shape

If a baseball card appreciates exponentially in value by 50% over 10 years, what is its annual appreciation (growth) rate? Please use a calculator, and answer to the nearest whole percent. ​

Answers

Using an exponential function, it is found that it's annual growth rate is of 4%.

What is an exponential function?

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

A(0) is the initial value.r is the growth rate, as a decimal.

In this problem, the card appreciates exponentially in value by 50% over 10 years, hence:

A(10) = 1.5A(0).

Thus:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]1.5A(0) = A(0)(1 + r)^{10}[/tex]

[tex](1 + r)^{10} = 1.5[/tex]

[tex]\sqrt[10]{(1 + r)^{10}} = \sqrt[10]{1.5}[/tex]

1 + r = 1.04.

r = 0.04.

0.04 x 100% = 4%.

It's annual growth rate is of 4%.

More can be learned about exponential functions at https://brainly.com/question/25537936


Can someone please help me I need it asap!! I’ll give brainlist !!!

Answers

Answer:

[tex]6^{6}[/tex]

Step-by-step explanation:

When the coefficient is the same (in this case it is 6), you can subtract the exponents when it's being divided.

So in this case, the exponents are 9 and 3. The 9 is being divided by the 3, So:

[tex]6^{9-3}[/tex]

[tex]6^{6}[/tex]

Jordan wants to put wire fence around each of his tomato plants. He has a partial roll of fencing which is 18 1/6 feet long. How many tomato plants will Jordan be able to put a fence around using this roll if each plant requires exactly 2 2/3 feet of fencing.

Answers

Answer:

6 tomato plants

Step-by-step explanation:

[tex]18\frac{1}{6}= \frac{18\times6+1}{6}=\frac{108+1}{6}= \frac{109}{6}[/tex]

[tex]2\frac{2}{3}= \frac{2\times3+2}{3}=\frac{6+2}{3}= \frac{8}{3}[/tex]

then the number of tomato plants that Jordan will be able to put a fence around using this roll :

[tex]\frac{\frac{109}{6}}{\frac{8}{3}}= \frac{109}{6}}\times\frac{3}{8} = \frac{109}{2}}\times\frac{1}{8}= \frac{109}{16} = 6.8125[/tex]

then he can put fence only around 6 plants.

Alex for school I need help whoever helps first will get brainlyist

Answers

Answer:

wheres the question ?

Step-by-step explanation:

A snack company can pack 12 granola bars in a box. How many boxes are needed for 600 granola bars?
A.5
B.720
C.50
D.7, 200

Answers

Answer:

The Answer is C. 50

Step-by-step explanation:

To pack 600 granola bars, 50 boxes are needed.

The correct option is C.

To determine how many boxes are needed for 600 granola bars, we divide the total number of granola bars by the number of granola bars that can be packed in one box.

Number of boxes = Total granola bars / Granola bars per box

Number of boxes = 600 / 12

Number of boxes = 50

So, 50 boxes are needed to pack 600 granola bars.

The correct answer is option C: 50.

To confirm this, let's see the reasoning: Since each box can hold 12 granola bars, to get 600 granola bars, you need to divide 600 by 12. The result is 50, which means you need 50 boxes to pack 600 granola bars. Option C, with 50, is the correct answer. Options A, B, and D do not provide the accurate number of boxes required for 600 granola bars.

To learn more about the division;

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