Let f(x)=5x^4 and g(x)=e^2x+x. If h is the function defined by h(x)=f(g(x)), which of the following gives a correct expression for h′(x)?

Let F(x)=5x^4 And G(x)=e^2x+x. If H Is The Function Defined By H(x)=f(g(x)), Which Of The Following Gives

Answers

Answer 1
Look it up on quizzes
Answer 2

The values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex]  (2[tex]e^{2x}[/tex] + 1 ).

Option C is the correct answer.

Given,

f(x)=5x^4 and g(x)=e^2x+x.

If h is the function defined by h(x)=f(g(x)),

We need to find h′(x).

What is the differentiation formula for the following?

We have,

dx/dx = 1

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

d[tex]e^{x}[/tex]/dx = [tex]e^{x}[/tex]

d[tex]e^{n}[/tex]/dx = [tex]ne^{n}[/tex]

d(cx)/dx = c(dx/dx) = c

We have,

- f(x)=5[tex]x^{4}[/tex] ______(1)
- g(x)=[tex]e^{2x}[/tex]+x ______(2)

- h(x)=f(g(x)) _______(3)

Now,

h(x) = f ( [tex]e^{2x}[/tex]+x )

From (1)

h(x) = 5[tex](e^{2x} + x) ^{4}[/tex] ______(4)

Now,

Differentiate (4)

h'(x) = 5 d[tex](e^{2x} + x) ^{4}[/tex]/dx

h'(x) = 5 x 4 [tex](e^{2x} + x) ^{3}[/tex] d [tex](e^{2x} + x)[/tex] / dx

h'(x) =20 [tex](e^{2x} + x) ^{3}[/tex] ( d[tex]e^{2x}[/tex]/dx + dx/dx )

h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex]  (2[tex]e^{2x}[/tex] + 1 )

Thus the values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex]  (2[tex]e^{2x}[/tex] + 1 ).

Option C is the correct answer.

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Related Questions

Lines AB and CD are parallel. Find the measures of the three angles in triangle ABF,Measurement of angle FAB

Answers

Answer:

not enough information

Step-by-step explanation:

in order to even think about solving this we need at 2/3 measurements

like aas, sas, sss ect

HELP WILL GIVE BRAINLIEST

Answers

Answer:

x = 128 degrees

Step-by-step explanation:

x and 52 make a linear pair, meaning they both equal 180 degrees.

Therefore, to solve x you can do:

x + 52 = 180

x = 180 - 52

x = 128 degrees

Eggs should equal 128. The reason why is because there’s a line and a line equals 180°. Once you know that you 1 80-52 and you would get 128.

Two sides of an equilateral triangle are labeled 12 inches and 3x - 6 inches. Find x.

Answers

Answer:

6

Step-by-step explanation:

In equilateral triangle, all the sides are congruent.

3x - 6 = 12

Add 6 to both sides

3x = 12 + 6

3x = 18

Divide both sides by 3

x = 18/3

x = 6

if you need help with algbrea
my googl hangouts is
hello
jazlyn
2279 g mail

Answers

Answer:

is it jazly 2279 together then g mail?

Step-by-step explanation:

The graph shows the height of a plant over time. What is the unit rate?

Answers

The unit rate is 1/5. The plant grows 1 inch per 5 days.

loan a banko Q Mr shatish took of $ 12000 from The interest of for annum gives 5% per 3 years 3​

Answers

Answer:

interest: 1,800

total: 13,800

Step-by-step explanation:

sorry to ask this late on Friday but stuck at home without a calculator Plllleeeaaassseee Hep me!!!!!!!!!!!!!!!!!!!!!!

5+842+6666+7432+84 x 4

Answers

Answer:(:

Step-by-step explanation:

15281

Write the expression without radicals, using only positive exponents.

Answers

Answer:

[tex](a^{2}+b^{2})^{1/3}[/tex]

Step-by-step explanation:

(a² + b²)^1/3

Any number to the power 1/2 means to square root the number

Any number to the power 1/3 means to cube root the number etc.

Help plz !!
What are the dimensions of AB?

Answers

Answer: c.2*1

Step-by-step explanation: in the picture

You need to remember two definitions.

First, the dimensions of a matrix are the number of rows by the number of columns. If a matrix has a row and b columns, it's an a*b matrix.

Second, before computing the product of two given matrices, you need to check an important condition.

If a matrix A has i row and j columns. And a matrix B has k row and l columns we can not apply the product AB only if j = k. In other words the numbers of columns of A (j) must be equal to the number of rows of B (k).

If this condition is checked, than the new matrix will be of dimensions : ixl

In our case i = 2, j = 3, k = 3, l = 1

So the dimensions will be 2x1 so the answer is C.

Good luck

Help pls the photo is up

Answers

Answer:

here it is plz mark me as brainliest

A bakery sells ,medium and large pies. The ratio small:medium:large is 3:5:2 .What fraction of the pies are large ?

Answers

2/8

there’s 8 total pies and among all of them, there’s only 2 large pies
so 2 large pies out of eight pies

as a cure to the epidemic that spread in the whole country, the department of health released a new drug that is subject for experimentation, supposed that c(t)=2tt+2 (in mg/ml) represents the concentration of a drug in a patient's blood stream in t hours, how concentrated is the drug after 2 hours of administration

Answers

Answer:

Your smart maybe

Step-by-step explanation:

3/7x2/3 ..........................

Answers

[tex] \frac{3}{7} \times \frac{2}{3} \\ \\ reduce \: \: the \: numbers \\ \\ \frac{1}{7} \times 2 \\ \\ calculate \\ \\ = \frac{2}{7} \\ \\ in \: alternate \: \: form \\ \\ 0.285714 \\ \\ hope \: it \: helps[/tex]

Answer:

2/7

Step-by-step explanation:

3/7 x 2/3

1. Multiply the numerators and denominators: 3 ×2 = 6, 7 × 3 = 21 --> 6/21

2. Simplify: 6/21 = 2/7

42 points giv away PLZ ANSWER RN (5/8+3/4) divided by (-2/3 - 5/6)

Answers

Answer:

when you divide you get -11/12

if you have a calculator you could add the 5/8 and 3/4

then add the -2/3 and the -5/6

then divide the first answer by the second answer

Answer:

[tex] \frac{( \frac{5}{8} + \frac{3}{4}) }{( - \frac{ 2}{3} - \frac{5}{6} )} \\ \\ \\ \frac{( \frac{5}{8} + \frac{6}{8}) }{( - \frac{4}{6} - \frac{5}{6} ) } \\ \\ \\ \frac{ (\frac{5 + 6}{8}) }{( \frac{ - 4 - 5}{6} )} = \frac{( \frac{11}{8} )}{( - \frac{9}{6} )} \\ \\ \\ \frac{11}{8} \div ( - \frac{9}{6} ) \\ \\ \\ \frac{11}{8} \times ( - \frac{6}{9} ) \\ \\ \\ \frac{11}{8} \times ( - \frac{2}{3} ) \\ \\ \\ \frac{11}{4} \times ( - \frac{1}{3} ) \\ \\ \\ = - \frac{11}{12} \\ \\ \\ = - 0.91666[/tex]

I hope I helped you^_^

please help me with this work

Answers

Answer:

Here is question number one's perimeter and area.

The points you are giving are really low so I will just do one

please help me with this maths questions

Answers

Answer:

yes in this problem u would multiply the exponents due to the parenthesis, equaling 5^18

A store had 2 BLUE chairs for $22.78 or 6 RED chairs for $67.80.

Type in the rate for each color of chairs below. blue $_______ Red $_______

Which color chair has a lower unit price? ________

Answers

Answer:

Blue chairs

Step-by-step explanation:

To get the unit rate of red chairs, you simply divide 22.78/2, which equals $11.39

So the unit rate of RED chairs is $11.39

To get the unit rate of the blue chairs, you simply divide 67.80/6 which equals $11.30

So the unit rate of BLUE chairs is $11.30

Unit rate is simply the cost of one item (in this case chairs) the unit rate stays the same. If we flipped the operation on blue chairs and did 11.30*6, it equals $67.80. The same goes for the red chairs, if we did 11.39*2 it equals $22.78.

Hope this helps!

if x = (7+4√3), then the value of x^2 + 1/x^2 is​

Answers

Answer:

194.

Step-by-step explanation:

x = (7+4√3)

x^2 =  x = (7+4√3)^2

= 49 + 48 + 56√3

= 97 + 56√3

x^2 + 1/x^2 =    97 + 56√3 + 1/(97 + 56√3)

= 194.

Help! Look at the image below!

Answers

Answer:

the answer is (6,9) so the answer for y is 9

Step-by-step explanation:

2x+34=6-5x pls help show work I’ll mark as brainliest!!

Answers

Answer:

x = -4

Step-by-step explanation:

2x + 34 = 6 - 5x

Subtract 34 from both sides.

2x = -28 - 5x

Add 5x to both sides.

7x = -28

Divide both sides by 7.

x = -4

Proof:

2x + 34 = 6 - 5x

Substitute variable.

2(-4) + 34 = 6 - 5(-4)

Multiply.

-8 + 34 = 6 + 20

Add.

26 = 26

Answer:

x = -4

Step-by-step explanation:

2x+34=6-5x

+5x +34 = 6+5x

------------------------

7x +34 = 6

7x -34 = -34

-----------------

7x = -28

---    ------

7       7

x = -4

Given the endpoint (-4,5) and midpoint (-8, 8), what is the other endpoint?

Answers

Answer: the endpoint is going to be  (-12,11)

Step-by-step explanation: sorry if it wrong

The quality assurance department at a gear found that there were 3 defective gears for every 500 produced. Write this as a fraction and as a precent. Please explain

Answers

Answer:

3/500

Step-by-step explanation:

3/500 I think it might be the 3/5000 because it just makes sense

Write the decimal as a fraction in simplist form -0.096

Answers

Answer:

Step-by-step explanation:

-0.096 is -0.096 thousandths, or -96/1000

That can be reduced by removing 8:

-[(8)*(12)]/[(8)*(125)] = -12/135

-12/125 = -0.096

3. Write the explicit definition for the sequence given

Answers

Answer: You did not give a sequence so I cannot help you.

Step-by-step explanation: try to copy and paste the entire sequence.

3. Which table has a constant of proportionality equal to 2.5?
x
х
y
X
0
0
2.5
os
2.5
NO
1
2
.
5
7.5
А
о
B
х
y
2
у
2.5
3.75
W NX
2
5
3
3
7.5
10
4
ch
5
4
D

Answers

Answer:

your answer is A

I can assure you that you will give brainlest

Answer:

A

Step-by-step explanation:

What is 9 plus 10???​

Answers

Answer:

21

Here’s legitimate proof that 9+10=21

(9 + 10) (base x) = 21 (base y)

9(1) + [1(x) + 0(1)] = 2(y) + 1

Simplify and solve for y:

2y = 8 + x

y = 4 + x/2

Since we have number bases, we want x and y to be positive integers. The term x/2 requires that x be a positive even number.

Also since 9 is in base x, we have x ≥ 10, as the digit 9 would not be used for a base 9 or smaller.

Thus we have the pairs of solutions:

x = 10, so y = 9

x = 12, so y = 10

x = 14, so y = 12

x, y = 4 + x/2 … Therefore 9+10=21!

Find the percent decrease. Round to the nearest percent.


From 99°F to 72°F

Answers

Answer:

Step-by-step explanation:

71.28

I’ll give brainliest if correct

Function A is represented by the equation y = 3x + 4.
Function B is a linear function that goes through the points shown in the table


A. The rate of change of function A is 3.The rate of change of function B is 10

B. The rate of change of function A is 3. The rate of change of function B is

C. The rate of change of function A is 4.The rate of change of function B is 10.


D. The rate of change of function A is 4. The rate of change of function B is 5.

Answers

Answer:

a

Step-by-step explanation:

What is the formula of speed?

Answers

Answer:

d/t

D= Distance

T= Time

Step-by-step explanation:

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The formula to find average speed ~

[tex] \mathrm{ \dfrac{total \: \: distance \: \: covered}{total \: \: time \: \: taken} }[/tex]

Formula for Instantaneous speed ~

[tex] \dfrac{ds}{dt} [/tex]

where,

s represents distance covered

t represents time

It's derivative of distance with respect to time ~

hope it helps !

According to her running log, Ariana averaged 4 miles per week last month and 75% less this month. How much did she average this month?

Answers

Answer:

She averaged 3 miles per week this month.

Step-by-step explanation:

You just take 75% of 4 and get 3.

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