Hi. I need help with these questions (see image)
Please show workings.
Question : Find the derivative with respect to x of each of the following:
(see image)
Answers
Answer:
see explanation
Step-by-step explanation:
Note that [tex]log_{e}[/tex] x = lnx ( natural logarithm)
Using the standard derivatives
[tex]\frac{d}{dx}[/tex] (lnx ) = [tex]\frac{1}{x}[/tex] , [tex]\frac{d}{dx}[/tex] ([tex]log_{a}[/tex] x ) = [tex]\frac{1}{xlna}[/tex]
Using the chain rule
Given y = f(g(x)) , then
[tex]\frac{dy}{dx}[/tex] = f'(g(x))) × g'(x) ← chain rule
(c)
y = [tex]log_{10}[/tex] (x² - 2) then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{(x^2-2)ln10}[/tex] × [tex]\frac{d}{dx}[/tex] (x² - 2)
= [tex]\frac{1}{(x^2-2)ln10}[/tex] × 2x
= [tex]\frac{2x}{(x^2-2)ln10}[/tex]
(d)
y = ln([tex]\frac{1}{x}[/tex] )
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{\frac{1}{x} }[/tex] × [tex]\frac{d}{dx}[/tex] ([tex]x^{-1}[/tex] )
= x × - [tex]x^{-2}[/tex]
= x × [tex]\frac{-1}{x^2}[/tex]
= - [tex]\frac{1}{x}[/tex]
Related Questions
I REALLY NEED HELP PLEASE ANSWER!!!!!
Answers
Answer:
an equation would be 2 + 2 = 4
Hope this helps
Step-by-step explanation:
What input will result in an output of 12 for the following functions d(x) = 2x -4
Answers
Answer:
8
Step-by-step explanation:
12=2x-4
12+4 = 2x
16 = 2x
16/2 =x
x =8
check
d(x) = 2(8)-4
=16-4
=12
+30 puntos.
1) 7 (x+3) 5x + 5
Answers
Step-by-step explanation:
[tex]7(x+3)5x+5 \\
(7x+21)5x +5 \\ 35 {x}^{2} + 105x + 5[/tex]
Expand the following
8.05 x 10^-2
a)80.5
b)0.805
c)0.0805
d)8.05
Answers
the product x3⋅x4. Both terms have the same base, x, but they are raised to different exponents. Expand each expression, and then rewrite the resulting expression. ... Write each of the following products with a single base. Do not simplify further. ... notation. a 3.547×1014; b −2×106; c 7.91×10−7; d −8.05×10−12 ..
10^-2 equal to 0.01
so 8.05×0.01 = 0.0805
or when you see 10^-2, the exponent -2 means to move the decimal point left twice, you get 0.0805
Find the value of x
Answers
Answer:
Hypotenuse x = 10 unit
Step-by-step explanation:
Given:
Two equal sides = 5√2
Find:
Hypotenuse x
Computation:
Using Pythagorean theorem;
Hypotenuse = √Base² + Perpendicular²
Hypotenuse x = √(5√2)² + (5√2)²
Hypotenuse x = √50 + 50
Hypotenuse x = √100
Hypotenuse x = 10 unit
Select the correct answer from each drop-down menu. Joshua charges $12.50 an hour for his tutoring services. He also charges the same rate for giving guitar lessons. On Saturday, Joshua drove to Eric's house to tutor him. To compensate for his traveling, Joshua charged a flat amount of $4.50 in addition to his hourly rates. For Saturday's session, Joshua earned a total of $35.75. On Sunday, Joshua gave Ben guitar lessons for 0.5 hour and tutored him for the remaining time. A flat rate for traveling was not charged. For Sunday's session, Joshua earned a total of $31.25. Complete the sentences. Joshua tutored Eric Ben. Joshua earned more on Saturday than on Sunday.
Answers
A band must pay a $2500 entrance fee, It will split the cost between its 25 members. How much will each member pay?
Please help quick
Answers
Answer $100 each
Step-by-step explanation:
2500/25
Answer: 2500/25
Each member pays $100
============================================
Explanation:
The slash symbol means division. It's the same as saying 2500 ÷ 25
The expression 2500/25 simplifies to 100, which means that each member must pay $100. If you had 25 members paying $100 each, then 25*100 = 2500 dollars is the total amount of money paid.
So in short, you divide the total cost over the number of members.
Is 3 a factor of 20b - 10?
yes
no
HELP ASAP
Answers
Answer:
No. To factor the answer would be 10(2b-1)
Step-by-step explanation:
Factor 10 out of 20b − 10.
Hoped this helped!
Are you that editor from tiktok?
A man receives a rate of $3.00 per hour for a 40-hour work week. If he receives 1.5 times the regular rate for overtime, how much will he earn working a 50-hour week?
Answers
Answer:
I NEED THE SAME ANSWER
Step-by-step explanation:
Simplify where possible 3 (x+3)
Answers
3(x+3)
3*x + 3*3
3x+9
divide by three to simplify
x + 3
if you’re supposed to solve it, subtract three
x = -3
PLS HELP: I am unsure how to calculate this into final numbers.
Cal Amity decided to survey 880 inhabitants of the Kingdom so that he could have a confidence level of 95% and a margin of error of 3%. He found that 72% of his sample answered "yes" to the second survey question, which was, "Have you done anything, or will you do anything, to prepare your kitchen for Gourmando's visit?"
Mr. Amity can infer that, most likely, between _[blank A]_ and _[blank B]_ inhabitants of the Kingdom have done, or will do something, to prepare their kitchen before Gourmando's visit.
Options:
blank A: 3450
blank B: 5000
blank A: 0
blank B: 300
blank A: 3600
blank A: 150
blank B: 3600
blank B: 3750
Answers
Complete question :
Cal Amity decided to survey 880 inhabitants of the Kingdom so that he could have a confidence level of 95% and a margin of error of 3%. He found that 72% of his sample answered "yes" to the second survey question, which was, "Have you done anything, or will you do anything, to prepare your kitchen for Gourmando's visit?"
Mr. Amity can infer that, most likely, between _[blank A]_ and _[blank B]_ inhabitants of the Kingdom have done, or will do something, to prepare their kitchen before Gourmando's visit.
If a population is 5000
Answer:
blank A: 3450
blank B: 3750
Step-by-step explanation:
Number of inhabitants surveyed = 880
Population size = 5000
Error margin = 3%
Percentage that answered 'yes' = 72%
The confidence interval :
Mean ± Error margin
Lower Bound = 72% - 3% = 69% = 0.69
Upper bound = 72% + 3% = 75% = 0.75
Since the question want us know the overall inhabitants of the kingdom who fall between this interval :
Blank A = lower boundary = 0.69 * 5000 = 3450
Blank B = upper boundary = 0.75 * 5000 = 3750
PLEASE HELP!!
Which inequality describes all the solutions to -5x + 6 -9
B. x 4
Answers
Answer:
-5x-3
Step-by-step explanation:
-5x+6-9=-5x-3
The inequality that describes all the solutions to the given inequality expression is x > 4
Given the inequality expression -5x + 6 < 2(-3 − x)
Expand the right-hand side of the ineqality
-5x + 6 < -6 - 2x
Collect the like terms
-5x + 2x < -6 - 6
-3x < -12
Divide both sides by -3
-3x/-3 > -12/-3
x > 4
Hence the inequality that describes all the solutions to the given inequality expression is x > 4
Learn more here: https://brainly.com/question/15816805
Write the x and y coordinates for points A, B, C, D, E,F,G,H
Answers
Answer:
A = (0, 1)
B = (2, 3)
C = (5, 7)
D = (8, 1)
E = (5, 0)
F = (-6, 5)
G = (-5, -2)
H = (-3, -6)
Subtract. Express your answer in lowest terms. 10 5/11 - 4 2/11
Answers
Answer:
6 3/11
Step-by-step explanation:
Subtract the whole numbers: 10 - 4 = 6
Subtract the fractions: 5/11 - 2/11 = 3/11
10 5/11 - 4 2/11 = 6 3/11
A train travels 40 km west in an hour. The train stops for another hour. Then, the train travels another 80 km west in two hours.
What is the velocity of the train?
a. 40 km/h
b. 30 km/h west
c. 40 km/h east
d. 30 km/h
Answers
Answer:
b.
Step-by-step explanation:
edge 2021
hope this helps
The velocity of the train is 30 km/h west.
Definition of velocityVelocity can be determined by dividing the total displacement travelled by the total time travelled. The direction of travel is also added.
Calculation of velocity Total displacement = 80 km + 40 km = 120 km Total time = 1 hour + 1 hour + 2 hours = 4 hours Direction = westVelocity = 120 km / 4 hours = 30 km/h west.
To learn more about velocity, please check: https://brainly.com/question/862972
A machine can make 14,400 screws in 8 hours. A second machine can make twice as many screws. What is the constant of proportionality (k) between the number of screws (y) and the number of hours (x) for the second machine?
Answers
Answer:
1800 screws per hour
Step-by-step explanation:
Find the quotient 25) 8525 A 215 B. 305 C 341 D. 2141 E 3041
Answers
Answer:
c
Step-by-step explanation:
because the product of 341 and 25 is 8525.
85 / 16 with a remainder
Answers
Answer:
the top number is the answer and the remainder is the bottom number in decimals its = 5.31
Step-by-step explanation:
hope this helped
The three angle measures in a triangle are congruent. The angles are equiangular! What is the measurement of one of the angles?
Answers
Answer:
60 degrees per angle.
Step-by-step explanation: a triangle has a total of 180 degrees, and the number of sides determine the number of angles it has. in this case, it's an equilateral triangle. 180/3 = 60. all triangles have 3 sides if you didn't know that ;)
75 = n + 12
Help pls
Answers
Answer:
n = 63
Step-by-step explanation:
75 - 12 = n
75 - 12 = 63
hope this helps...
Answer:
n = 63
Step-by-step explanation:
We have: n+12 = 75
Subtract 12 from both sides and we get: n = 63
Match the symbol with its corresponding category.
Answers
Answer:
N-Natural
R-Real
Z-integer
Q-rational
As an estimation we are told £3 is €4.
Convert €32 to pounds.
help pleaseeee!
Answers
Please help me. I really don't know dis
Answers
Answer:
I would do C because 2/3 is close to a whole so then you would get -3 and 1/4 is close to 0 so just keep 18 the same which would be -18 so -18 divided by -3 would be correct
Step-by-step explanation:
A regular polygon has 12 sides find the size of each of its interior angles
Answers
Answer:
150°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° ( n - 2) ← n is the number of sides
Here n = 12, then
sum = 180° × 10 = 1800°
Since there are 12 interior angles, then
size of each interior angle = 1800° ÷ 12 = 150°
Write the equation of a vertical line running through the point (-2,-10)
Answers
can i plz get some help
Answers
2. 1 and 5, 2 and 6, 3 and 7, 4 and 8
3. Alternate interior angles
4. Not sure about this one
5. Alternate exterior angles
6. Vertically opposite angles
7. Interior opposite angles
8. Alternate interior angles
9. Corresponding angles
10.alternate exterior angles
help please :/ i might die if i don’t get helpppp
Answers
Which set of ordered pairs is a function?
A {(-1,5), (-1,4).(-1,3), (-1,2).(-1,1)}
B {(-6,-4).(-4,-2), (0,0).(-4,2).(-6,4)}
C {(-5,1). (-3,2).(-1,3), (1,4), (3,5)}
D {(-2.1).(-4,2), (0.3). (4.1).(-2,5)}
Answers
Answer: i think A
Step-by-step explanation:
PLEASE HELP!!! I NEED TO TURN THI IN SOON !!!
Question and instructions in the image below!!!
MAKE SURE TO JUSTIFY YOUR ANSWER!!!!
Will mark brainliest if correct!!!
Answers
Answer:
3. f(x + 3)Step-by-step explanation:
Point A is 3 units to the left from the graph
The graph, if translated 3 units to the left will include the point A.
Horizontal translation is:
f(x) ⇒ f(x + 3)Correct option is 3.
Answer:
3. f(x + 3)
Step-by-step explanation:
On a map 1 centimeter represents 200 meters .Ridge Trail is 850 meters long. How long is Ridge Trail on the map?
Answers
Answer:
hmmmmmm
Step-by-step explanation: