Answers
This is the same as typing in 0.5x^7
Other equivalent forms are (1/2)x^7 or (x^7)/2
=====================================================
Work Shown:
[tex]\frac{d}{dx}\left[f(x^2)\right] = x^8\\\\f'(x^2)*\frac{d}{dx}(x^2) = x^8\\\\f'(x^2)*2x = x^8\\\\f'(x^2) = \frac{x^8}{2x}\\\\f'(x^2) = \frac{x^7}{2}\\\\f'(x^2) = \frac{1}{2}x^7\\\\f'(x^2) = \boldsymbol{0.5x^7}\\\\[/tex]
I used the chain rule on the second step. The chain rule will apply the derivative to the outer function f(x^2). Then we also apply the derivative to the inner function x^2 to get 2x, which is multiplied with f ' (x^2). From that point, we isolate f ' (x^2).
Side note: When applying the first derivative, it might help to think of f(x^2) as simply f(x) on a temporary basis.
Related Questions
If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.
Answers
Answer:
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]
Step-by-step explanation:
[tex]\frac{dx}{dt}=2[/tex]
[tex]\frac{d\theta}{dt}=?[/tex]
[tex]x=12[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]cos(\theta)=\frac{12}{13}[/tex]
[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]
The value of θ is given by the inverse sine function, from which the rate of
change of θ with respect to x can be derived.
The rate of change of θ at the instant when x = 12 units is -0.4 rad/sReasons:
[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]
[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]
[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]
[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]
Using chain rule of differentiation, we have;
[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]
Therefore;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]
When x = 12, we get;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]
The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s
Learn more about rate of change here:
https://brainly.com/question/24686935
derivative for the function of t3+k/t=
Answers
Answer:
Step-by-step explanation:
I will ASSUME you want the derivative with respect to "t" of the equation
f(t) = t³ + kt⁻¹
f'(t) = 3t² - kt⁻² which can also be 3t² - k/t²
Help I need help solving this!
Answers
Answer:
Step-by-step explanation:
I want to know how to find the area of polygon.
Answers
Answer:
The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].
Step-by-step explanation:
{NOBITA}
Answer:
To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Find the apothem of the polygon. If you're using the apothem method, then the apothem will be provided for you. Let's say you're working with a hexagon that has an apothem with a length of 10√3.
Step-by-step explanation:
but for a rectangle the area formula is
width*height
for a trapezoid area formula is 1/2(base1+base2)*height
for a hexagon area formula is
area = (3/2) · sqrt(3) · s2
please help ill mark brainliest
Answers
Answer:
Pretty sure it is SAS as the angles are congruent
Step-by-step explanation:
Answer:
number 4
Step-by-step explanation:
both triangles use the aa as a point
Sofia walks from her house to the park. She reaches the park at 5 5 : : 25 25 . If it is a 40 40 -minute walk, what time did she leave her house?
Answers
Answer:
4:45
Step-by-step explanation:
hope this helps
I been on this for days and no one can give me a right answer
Answers
Answer:
2x²=6x-5= x=3+i/2
-x²-10x=34= x = -(5+3i)
Step-by-step explanation: 2x²=6x-5 and -x²-10x=34 are the answers
There are 110 students on the team. 100% of them will be off for break. How many students are on break?
Answers
Answer:
110
Step-by-step explanation:
100% of 110 means all of 110, which is just 110.
Are you sure you didn't make a typo here because I'm pretty sure this wouldn't be given on a homework. Just wondering.
Ten men and ten women are to be put in a row. Find the number of possible rows if Beryl, Carol, and Darryl want to stand next to each other in some order (such as Carol, Beryl, and Darryl, or Darryl, Beryl and Carol).
Answers
Answer: 6 possibilities.
Carol, Beryl, and Darryl
Carol, Darryl, and Beryl
Darryl, Carol, and Beryl
Darryl, Beryl, and Carol
Beryl, Darryl, and Carol
Beryl, Carol, and Darryl
Hope this helps :)
Keri has some ball bearings. Each one is in the shape of a sphere with a radius of 6 mm.
(a) Find the volume of one ball bearing. Give your answer in mm3 in terms of pi
Answers
I have a Statistics question
Answers
Answer:
we're your question
Step-by-step explanation:
again please
Answer:
Yes
Step-by-step explanation:
what is it
I need help please I don’t know what to it is due today
Answers
Answer:
12 blue necklaces + 12 red necklaces = 24 necklaces. He will have 1 blue bead left over and 1 red bead left over.
Step-by-step explanation:
37/3 = 12.333 or 12 r1
25/2= 12.5 or 12 r1
1+1=2
The football team has a total of 350 jerseys. There are 154 medium-sized jerseys. What percent of the jerseys are medium-sized jerseys?
Pls help me
Answers
Answer:
Step-by-step explanation:
Given : The total number of jerseys = 350
The number of medium-sized jerseys = 154
Then, the percent of the jerseys are medium-sized jerseys will be :-
\begin{gathered}\dfrac{\text{Number of medium-sized jerseys }}{\text{Total jerseys}}\times100\\\\=\dfrac{154}{350}\times100\\\\=0.44\times100=44\%\end{gathered}
Total jerseys
Number of medium-sized jerseys
×100
=
350
154
×100
=0.44×100=44%
Therefore , the percent of the jerseys are medium-sized jerseys = 44%
Which equation below compares the amount of medicine, S, in Sofia’s system with the amount of medicine, L, in Lexi’s system? L = 16 x S S = 16 x L L = 4 + S S = 4 + L
Answers
Answer:
L=16xS
Step-by-step explanation:
The bar chart shows the number of students with each letter grade in a certain professor's math classes. Since students need at least a C for the grade to transfer, the professor groups all grades that are less than C into one category instead of grouping D's and F's separately.
How many fewer students have less than C's than have C's?
A 212
B 612
C 123
D 89
Answers
Answer:
Since students need at least a C for the grade to transferdes that are less than C into one category instead of grouping D's and F's separately. How many ...
Inequality word problem
Step by step and explanation pls do the problem or report
Answers
Answer:
34 hours or more
Step-by-step explanation:
If h is the number of hours Jack works, then his earnings will total 15h. He wants that to be at least 500. The appropriate inequality is ...
15h ≥ 500
h ≥ 33 1/3 . . . . . divide by 15
Jack needs to work 34 hours or more to earn at least $500.
What is the volume of a cone
Answers
2 x 5 x 0 please help
Answers
0
0 multiplied by anything is going to always be 0
A= 1/2bh
solve for b
Answers
Ok done. Thank to me :>
Answer:
A = bh ( multiply both sides by 2 to clear the fraction )
2A = bh ( divide both sides by h )
b=2A/H
Step-by-step explanation:
For each equation find a value for x that makes the equation true 10=3x-6
Answers
Answer:
5.3333
or 5 and 1/3
Step-by-step explanation:
10 = 3x - 6
add six
16 = 3x
divide by 3
5.3333 = x
I hope this helps!!
The Smith family goes out for lunch, and the price of the meal is $45.The sales tax on the meal is 6%, and the family also leaves a 20%tip on the pre-tax amount. What is the total cost of the meal?
Answers
Answer:
$56.70
Step-by-step explanation:
45 x 6% = 2.7 Multiply price of meal with the percentage of sales tax
45 x 20% = 9 Multiply price of mean with the percentage of tip
$9 is the tip amount
$2.70 is the sales tax
$45 + $2.70 + $9 = $56.70. Add the price of the meal with the sales tax and tip amount to get the total cost of the meal.
Hello hello helppppppppppppp
Answers
5 units left and 2 units down
Answer:
the person anove is correct
Step-by-step explanation:
Kripa’s father is 35 years younger than her grandfather, and 40 years older than her. If the sum of the ages of the three is 160 years, let’s find her grandfather’s age?
Answers
Answer:
90 years
Step-by-step explanation:
if Kripa's age = x
Father's age = x + 40
Grandfather's age = (x + 40) + 35 = x + 75 (father is 35 years younger than grandfather i.e. grandfather is 35 years older than father)
x + x + 40 + x + 75 = 160
=> 3x = 160 - 115
=> x = 45/3 = 15
grandfather's age = x + 75 = 90 years
Answer:
90 yearsStep-by-step explanation:
x + x + 40 + x + 75 = 160
=> 3x = 160 - 115
=> x = 45/3 = 15
Grandfather's age = x + 75 = 90 years
is 0.75 degrees Celsius a negative temperature or positive temperature
Answers
Answer:
Positive
Step-by-step explanation:
Anything below 0 is negative. 0.75 > 0
If A = -3n + 2, and B = 5n - 7, what is the value of A - B, in simplest form?
Answers
Answer:
2n-5
Step-by-step explanation:
So you would combine your like terms witch would be -3n+5n which would give you 2n then you would do 2-7 and get -5 then you get you answer 2n-5
The value of (A - B) in the simplest form is (A - B) = -8n + 9.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equations are A = -3n + 2 and B = 5n - 7.
The value of A - B is:
A - B
= -3n + 2 - (5n - 7)
= -3n + 2 - 5n + 7
= -8n + 9
Hence, the value of (A - B) in the simplest form is (A - B) = -8n + 9.
Learn more about equations here:
https://brainly.com/question/10413253
limx→0
tan x − x
x − sin x
Answers
Answer:
Please understand me download an math algebra in play storeanswer thisssssssssssssss
Answers
ACE = 115
angles ABC and DCB are congruent because they are alternate interior angles
DCB =35
and for angle ACB we do
ACE + ACB + DCB = 180
115 + ACB + 35 = 180
ACB = 180 - 115 - 36
ACB = 29
Help!!!!!!please help i will fail
Answers
Answer:
WHAT is to solve their is notting
Step-by-step explanation:
PLEASE HELP!!!
True or false
3(x-2) and 3x-6 are
equivalent
Answers
Answer:
true!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
True.
Step-by-step explanation:
They are equivalent expression because if you distribute the 3 in 3(x-2), you will get the same expression as 3x-6.
3(x-2) =
(3*x) - (3*2) =
3x - 6
Hope this helps.
9. What conversion factor can you use to convert miles to inches? Explain how you found it.
Answers
Answer:
You know that 1 mile = 5280 feet and 1 foot = 12 inches, so using these conversion factors you can go from one to the other.
I hope this answered you question!
Step-by-step explanation: