Please help and I have to do this as soon as possible

[tex]\text{Given that,}\\\\\\f(x) = \ln(x^4 +e^{2x})\\\\\\f'(x) = \dfrac{1}{x^4 + e^{2x}} \left(4x^3+2e^{2x}\right) = \dfrac{2(2x^3+e^{2x})}{x^4 + e^{2x}}~~~~;[\text{Chain rule}]\\\\\\\text{Note:}\\\\\dfrac{d}{dx} \ln x = \dfrac 1x\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} e^{mx} = m e^{mx}[/tex]

After solving the given equation, the value obtained is equal to [tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex].

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given data in the question,

f(x) = ln (x⁴ + e²ˣ)

[tex]f'(x)=\frac{1}{x^4+e^2^x}(4x^3+2e^2^x)[/tex]

Now, use the chain rule,

[tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex]

Also, note some points,

d/dx ln (x) = 1/x

[tex]\frac{d}{dx}x^n=nx^n^-^1[/tex]

To know more about Expression:

https://brainly.com/question/14083225

#SPJ2

Answer:

6:4:3

Step-by-step explanation:

each can be divided by 7

Answer:

6 4 3

Step-by-step explanation:

Δ PQR has: PM is a median

so: MR = QM = 3 cm

ANSWER: MR = 3 cm

Ok done. Thank to me :>

Answer: yes they are

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

all angles add up to 180*, 180-90=90, 90=3x, 30=x

Answer:

x = 30

Step-by-step explanation:

One side is 90 so the other two sides have to add up to 90 too because a triangles' angles have to add up to 180.

So, we can write that 2x + x = 90

Then we can solve for x:

2x + x = 90

3x = 90

x = 30

Answer:ITS THE SECOND ONE

Step-by-step

Answer:

solution given:

let's see only in a right-angled triangle Δ ACD.

AC=3 units

AD=5 units

since Δ ACD is a right-angled triangle. It satisfies Pythagoras law

[tex]AD^{2}=AC^{2}+CD^{2}[/tex]

25=9+[tex]CD^2[/tex]

[tex]CD^2[/tex]=25-9=16

[tex]CD=\sqrt{16} =4 units[/tex]

Now

Area of rectangle Δ ACD=[tex]\frac{1}{2} CD*AC=\frac{1}{2}*4*3=6\: square \:units[/tex]

similarly,

[tex]\frac{1}{2} AD*CE=6\: square \:units\\ 5*CE=6*2\\CE=\frac{12}{5}=2.4 units[/tex]

since AB=CE=2.4 units

Δ ACE is a right-angled triangle. It satisfies Pythagoras law.

[tex]AC^{2}=AE^{2}+CE^{2}\\3^2=AE^2+2.4^2\\9-5.76=AE^2\\AE and BC=\sqrt{1.24} =1.11 units[/tex]

now

area of trapezoid=area ofΔACD+Area of ΔABC

=6+[tex]\frac{1}{2}AB*BC=6+\frac{1}{2}*2.4*1.11=6+1.33 =7.33\: square \:units[/tex]

Answer:

-1.5

Step-by-step explanation:

Answer:

350

Step-by-step explanation:

Write out the equation

d + d + 70 + d + 154 = 1274

Simplify

3d + 224 = 1274

Solve

3d = 1050

d = 1050 / 3

d = 350

Answer:

350

No probelm

[tex]x+x(2x)=x+2x^2\\\\\text{when x =2}\\\\2+ 2(2)^2 = 2+ 2(4) = 2+ 8 = 10[/tex]

[tex]\text{So, the answer is (a).}[/tex]

Answer:

1. 1[tex]\frac{1}{2}[/tex]

2. 1[tex]\frac{3}{10}[/tex]

3. [tex]\frac{1}{3}[/tex]

4. 1[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

I hope this helps!!

It would take 70 years for the deer population to reach 800.

An exponential function is in the form:

y = abˣ

where b is the multiplier, y, x are variables and a is the initial value.

Let y represent the population and x represent the time in years.

a = 200, b = 100% + 2% = 102% = 1.02

y = 200(1.02)ˣ

For a population of 800:

800 = 200(1.02)ˣ

ln(4) = xln(1.02)

x = 70 years

It would take 70 years for the deer population to reach 800.

Find out more on exponential function at: brainly.com/question/2456547

Answer: 200, 0.02, and 800

Step-by-step explanation:

Answer:

Solve for n

n=log5  (− 2 /y  −20x−5),y<−40x−10

Step-by-step explanation:

Answer:

36n + 18

Step-by-step explanation:

6 * 6n = 36n

6 * 3 = 18

36n + 18 = 36n + 18

Answer:

36n+18

Step-by-step explanation:

6(6n+3)

(6×6n)+(6×3)

36n+18

But if you want it simplifed, you can divide both 36n and 18 by 18 and you will be left with 2n+1

Step-by-step explanation:

1 _21:00_ , _22:10_, 1:10

2. 1:20

3. 18:00

4. 21:35

1. 21:00, 22:10, 1 hr and 10 minutes

2. 20 minutes

3. 18:40

4. 21:35

Answer:

[tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

Step-by-step explanation:

Because x=1 and x=4 are the solutions to x-1=0 and x-4=0, then we have (x-1)(x-4) in the denominator.

Because (-1,0) and (-6,0) are the solutions to x+1=0 and x+6=0, then we have (x+1)(x+6) in the numerator.

Now we have [tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex] where we plug in (0,8) to solve for a:

[tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex]

[tex]8=\frac{a(0+1)(0+6)}{(0-1)(0-4)}[/tex]

[tex]8=\frac{6a}{4}[/tex]

[tex]32=6a[/tex]

[tex]\frac{32}{6}=a[/tex]

[tex]\frac{16}{3}=a[/tex]

Therefore, the equation for the rational function is [tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

Answer:

It does not matter, since, from your second case, [tex]5\sqrt5 +11 = 11+5\sqrt5[/tex].

In general is a matter of personal preference but in general I like to start with a positive number (I like [tex]\sqrt2 -1[/tex] more than [tex]-1+\sqrt2[/tex] since if there's an equal sign before I'm guaranteed to have the two signs mesh together in a few steps).

If everything you are adding together is positive, I just go first come first served and pick a new term in order it appears in the previous passage.

Answer:

linear

Step-by-step explanation:

Answer: The answer is Iπ + √17|.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(3-1)^2+(-4-1)^2}\implies d=\sqrt{2^2+(-5)^2}\implies d = \sqrt{29}[/tex]

Answer:

D

Step-by-step explanation:

Cosine is adjacent / hypotenuse, so 12/13

Answer:

yes this right cuz ye or nah?

Step-by-step explanation:

yes cuz 0 1 2 3 4 5 6 7 8 9 are the numbers

Answer: [?] is 6

Step-by-step explanation:

x=5

so, 2x=10

10-4 is 6

Answer:

The number 9490 is called the numerator or dividend, and the number 5 is called the denominator or divisor.

The quotient of 9490 and 5, the ratio of 9490 and 5, as well as the fraction of 9490 and 5 all mean (almost) the same:

9490 divided by 5, often written as 9490/5.

Read on to find the result of 9490 divided by 5 in decimal notation, along with its properties.

Answer:

17

Step-by-step explanation:

Let the smaller number = x

Let the larger number = y

y = 2x + 8

y - x = 25                Add x to both sides

y = x + 25               Substitute this into the first equation

x + 25 = 2x + 8       Subtract 8 from both sides

x + 25 - 8 = 2x        Combine

x + 17 = 2x               Subtract x from both sides.

17 = 2x - x                Combine

17 = x