Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a correct process for finding h' (x) ?

Answers

Answer 1

Answer:

[tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

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⁻¹

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 h(x) = [2 + f(\sin x)]''[/tex]

Step 2: Differentiate

Derivative Rule [Chain Rule]:                                                                       [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [2 + f(\sin x)]'[/tex]Rewrite [Derivative Property - Addition/Subtraction]:                                 [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' \bigg[(2)' + [f(\sin x)]' \bigg][/tex]Derivative Rule [Basic Power Rule]:                                                             [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [f(\sin x)]'[/tex]Derivative Rule [Chain Rule]:                                                                       [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' f'(\sin x)(\sin x)'[/tex]Trigonometric Differentiation:                                                                       [tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

From here, if you would like, you can take the 3rd derivative of the last piece.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation


Related Questions

A line has a slope of 3 and passes through the point (8, 261. What is the
equation of the line?

Answers

Answer:

Step-by-step explanation:

We know that the form of line passing through point (x₀ , y₀) and having slope m is :

 y - y₀ = m(x - x₀)

Here the line passes through the point (5 , -3)

⇒ x₀ = -2 and y₀ = -5

Given : Slope(m) = -8

Substituting all the values in the standard form, We get :

Equation of the line : y + 3 = -8(x - 5)

solve similar triangles (advanced)

Answers

Answer:

x = 3/2

Step-by-step explanation:

ΔACB ≈ ΔAED due to hypotenuse-leg theorem

therefore, BC/BA = DE/AD

4/6 = 5/(x+6)

cross-multiply to get:

4(x+6) = 6(5)

4x + 24 = 30

4x = 6

x = 6/4 or 3/2

check:

4/6 = 5/7.5; the cross-products are both equal to 30

See attachment for question

Answers

I can’t see the attachment?

Write an expression to model each situation.


Sandra picked 10 blue flowers and 16 red flowers. Then she divided the flowers equally into 2 bouquets. _______________



A recipe called for 2/3 cup flour. Kyle doubled the recipe. Then he added 1/4 cup more flour to make the dough less sticky. ________________

Answers

The first one should be:
(10 + 16) ÷ 2
because if you didnt have any parentheses, it would have a different answer.

the second one should be:
2/3 x 2 + 1/4

For the given conditions expressions 1 and 2 are obtained as (10 + 16) ÷ 2 and 2/3 x 2 + 1/4 respectively.

What is a mathematical expression?

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression

It is given that the expression is,

Sandra selected 16 red flowers as well as 10 blue blooms. She then equally split the flowers into 2 bouquets.

The expression for the given condition is,

=(10 + 16) ÷ 2

If a recipe required 2/3 cup of flour. The recipe was quadrupled by Kyle. He then increased the flour by 1/4 cup to make the dough less sticky. The expression for the given condition is,

=2/3 x 2 + 1/4

Thus, the obtained expressions are (10 + 16) ÷ 2 and 2/3 x 2 + 1/4.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ2

Ben’s father is paying for a $20 meal he has a 50% off coupon for the meal after the discount a 7% sales tax is applied what does Ben’s father pay for the meal after the discount

Answers

$20 = 100%
50%= $10
Making $10 the new 100%
$10/100=0.1
0.1=1%
0.1x7=0.7
Meal after discount = $10.70
I think this is right? I hope it helped :)

the height and diameter of a cylinder are 21 cm and 12 cm. find the volume of cylinder

Answers

Answer:

the answer is 6930 cm3.

Step-by-step explanation:

please mark my answer in brainlist

3. If the diameter of “Frosty the Snowman’s” hat is ten inches, what’s the radius?

Answers

The radius is 5 inches

The cashier read the totals: $33.83, $19,40, $43.50, $3.08, $2.40. Circle the number that is wrong and record what it should be explain how you corrected the mistake

Answers

Answer:

74.0 g/mol

Explanation:

Step 1: Write the generic neutralization reaction

HA + NaOH ⇒ NaA + H₂O

Step 2: Calculate the reacting moles of NaOH

At the equivalence point, 33.83 mL of 0.115 M NaOH react.

0.03383 L × 0.115 mol/L = 3.89 × 10⁻³ mol

Step 3: Calculate the moles of HA that completely react with 3.89 × 10⁻³ moles of NaOH

The molar ratio of HA to NaOH is 1:1. The reacting moles of HA is 1/1 × 3.89 × 10⁻³ mol = 3.89 × 10⁻³ mol.

Step 4: Calculate the molar mass of the acid

3.89 × 10⁻³ moles of HA have a mass of 0.288 g.

M = 0.288 g / 3.89 × 10⁻³ mol = 74.0 g/mol

you need to really explain more and not going in person

find the circumference of a cd that has an diamater of 5 round your andwer to the nereast tenth

Answers

Answer:

15.7

Step-by-step explanation:

C = 2πr

C = 2(3.14)(2.5)

C = 15.7

Quadrilateral MNOP was dilated with the origin as the center of dilation to create quadrilateral M'N'O'P'. The quadrilateral was dilated using a scale factor of 1.5. The coordinates of the vertices of quadrilateral MNOP are given. What are the coordinates of N'?
A) (4,5)
B) (1.5, 2)
C) (4.5, 5.25)
D) (2, 2.3)

Answers

With the center of dilation at the origin, the image is given by the product

of the corresponding point on the preimage and the scale factor.

The coordinates of N' is; [tex]\underline{C) \ (4.5, \ 5.25)}[/tex]

Reasons:

The center of dilation of quadrilateral MNOP = The origin

The image following the dilation of MNOP = M'N'O'P'

The scale factor of dilation = 1.5

Required:

The coordinates of N'

Solution:

The coordinates of N in MNOP = N(3, 3.5)

The coordinate of a point (x', y') on the image following the dilation with center at the origin, of the preimage (x, y) by a scale factor is given as follows;

(x', y') = Scale factor × (x, y)

Which gives;

The coordinates of N' = 1.5 × N(3, 3.5) = N'(1.5 × 3, 1.5 × 3.5) = N'(4.5, 5.25)

The coordinates of N' = C) (4.5, 5.25)

Learn more about dilation transformation here:

https://brainly.com/question/12561082

Answer:

C) (4.5, 5.25)

Step-by-step explanation:

NEED HELP NOW PLEASE

Answers

Answer:

-33.24 degrees F, -33.625 degrees F, -33.833 degrees F

which pairs of polygons are congruent?

A. 3 and 4

B. 1 and 3

C. 1, 3, and 4

D. 2, 3, and 4

E. 1, 2, 3 and 4

Answers

Answer:

B

Step-by-step explanation:

I do not know how to answer these questions, can someone explain what I would do to solve them? ​

Answers

Answer:

Step-by-step explanation:

Which of the following is a solution of x2 + 2x + 4?

Answers

Answer:8x

Step-by-step explanation:

2++2=4 add x up 4 = 8x

Do you mean 2x for the first term or x^2? If the first term is 2X then the solution would be 4x+4. If the first term is not 2x but x^2 instead, then there is no solution for it

help i have math homework and im real bad at it i got a B- last year so help

Answers

4y-12 is the answer
4y-12 is correct. whatever number is outside of the parentheses you just multiply that with the two numbers in the parentheses to distribute :)

Multiply (x^2 + 4x) (x^3 - 2x^2 + x + 7)

Answers

Answer:

x^5+2x^4-7x^3+11x^2+28x

Step-by-step explanation:

Dez was called to solve a problem on the whiteboard in class. His work is shown below.

0.8 × Four-fifths

8/10 × 4/5 = 32/5

StartFraction 32 over 5 EndFraction = 6Two-fifths

Is the answer shown reasonable?

(A) The answer is reasonable because 0.8 was converted to an equivalent fraction.
(B) The answer is reasonable because it is greater than both factors.
(C) The answer is not reasonable because 4/5 of a number should be less than the number.
(D)The answer is not reasonable because StartFraction 32 over 5 EndFraction does not equal 6Two-fifths.

HELP ME PLZ!!!!!

Answers

Answer:

C. The answer is not reasonable because 4/5 of a number should be less than the number

Step-by-step explanation:

On Edge

help ASAP please which too answers are correct ​

Answers

Answer:

20 (30 + d)

Step-by-step explanation:

your welcome :)

Answer:

2 and 4th one.

Step-by-step explanation:

Hopes This Helps :)

Find the change in profit in dollars for each owner.
A. –43,200
B. 675
C. –675
D. 5,39

Answers

I read the question, and I am unable to answer that
I need to know other things besides the profit for each owner
I need to know the prior accounting period's profit for each owner

Perform (3x3 – 2x2 + 3x – 4) ÷ (x – 3) to find the value of the remainder.
A) 78
B) 68
C) 88
D) 98

Answers

C) 88

Explanation: trust me

Answer:

B.68

Step-by-step explanation:

divide using polynomial long division

1. You are planning an extended trip to Mexico. You have a new smartphone to keep in touch with your friends but are concerned about the roaming charges since you will be outside the home network service area. Your plan costs $40.00 per month plus $0.35 per minute for roaming charges. Write a linear model relating your monthly cost, C, and the roaming minutes, t.

A: C = $40 + $0.35t
B: C = $40 $0.35t
C: C = $0.35 + $40t
D: C = $0.35 $40t

Answers

a. $40 is the set price per month and $.035 is the changing rate per minute. If t represents the minutes you use the phone, then you have to multiple that amount by $.035

Kate and Elena were playing a card game. The stack of cards in the middle had 25 cards in it to begin with. Kate added 5 cards to the stack. Elena then took 8 cards from the stack. Finally, Kate took 7 cards from the stack. How many cards were left in the stack?

Answers

Answer:

15

Step-by-step explanation:

step 1: 25+5=30

step 2: 30-8=22

step 3:22-7=15

stions 5-7 the Grade 6 pupils graduated? In a school of 680 Grade 6 pupils, 646 graduated. What percent of the Grade 6 pupils graduated ? ​

Answers

Answer:

95% of Grade 6 pupils graduated

Answer:

95% of Grade 6 Pupils Graduated

Step-by-step explanation:

Express the Statement Mathematically:

646/680

Add Percentage

646/680 * 100%

By Division

0.95 * 100%

Then, Multiply

95%

#3: Classify the number below. Select all that apply.

-8

A. Real Number
B. Irrational
C. Rational
D. Integer
E. Whole
F. Natural

Answers

The answer would be C and D

What is the slope of the line that contains these points?

Slope:

Answers

Answer:

-4

Step-by-step explanation:

Slope formula:

m=y2-y1/x2-x1

I will use (-1,10) and (1,2)

2-10/1-(-1)

Which is

-8/2

Divide:

-4

Thus the slope is -4

Hope this helps!

How would I solve this?

Answers

Answer:

2a+3b=4a-3b

a+3=4b

b=3

a=9

Step-by-step explanation:

2a+3b=4a-3b

-2a=-6b

a=3b

a+3=4b

3b+3=4b

3=b

a=9

Today 90 students bought lunch from the cafeteria. If this was 60% of the students, how many students are there in total?

Answers

Answer:  150 students

Step-by-step explanation:

Let X be the total number of students.  We are told that:

0.60X = 90 students

X = (90 students)/0.60

X = 150 students

1. Classify the following polynomials as monomial, binomial trinomial and polynomial.
i) 7ab – 5a

Answers

Answer:

it's binomial...............................

It is binomial hope this helps

I need help on this question. please help me.. I don't have idea on this.​

Answers

Answer:

D.

Step-by-step explanation:

5(-4 +10) × 4.8 ÷ [tex]\frac{3}{4}[/tex]

5(6) × 4.8 ÷ [tex]\frac{3}{4}[/tex]

30 × 4.8 ÷ [tex]\frac{3}{4}[/tex]

30 × 4.8 × [tex]\frac{4}{3}[/tex]

_________________________________

Hope this helps!!

If I have made a mistake, please let me know; I enjoy leaning from them:)

Answer:

Step-by-step explanation:

can someone help me pleasee

Answers

Answer:

Erich planted 7 seeds ...

he had to remove 17 plants ....

he expected to have less or equal 46 plants ...

Step-by-step explanation:

Look at keywords like remove ~ => which indicates that something is being subtracted

Since x represents seed packets, and the amount he planted is a number multiplied by x, we can deduce he planted 7 seeds ( 7 * x)

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