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)?
Answers
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.
Learn more about differentiation here:
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Related Questions
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
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
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
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!
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!
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
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:
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
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
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.
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:
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
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.
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^_^
A bakery sells ,medium and large pies. The ratio small:medium:large is 3:5:2 .What fraction of the pies are large ?
Answers
there’s 8 total pies and among all of them, there’s only 2 large pies
so 2 large pies out of eight pies
The graph shows the height of a plant over time. What is the unit rate?
Answers
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:
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
Help pls the photo is up
Answers
Answer:
here it is plz mark me as brainliest
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.
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.
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
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:
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
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 timeIt's derivative of distance with respect to time ~
hope it helps !
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:
Find the percent decrease. Round to the nearest percent.
From 99°F to 72°F
Answers
Answer:
Step-by-step explanation:
71.28
Help! Look at the image below!
Answers
Answer:
the answer is (6,9) so the answer for y is 9
Step-by-step explanation:
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