Hello! :)
[tex]\large\boxed{\frac{dy}{dx} = 3^{(2x^{2} - 1)} (4x^{2}ln3 + 1)}[/tex]
Use the Product Rule to solve for the derivative:
[tex]\frac{dy}{dx}= f(x) * g'(x) + g(x) * f'(x)[/tex]
We can divide the expression into two different functions:
[tex]f(x) = x\\\\g(x) = 3^{2x^{2} -1}[/tex]
Use the Product Rule equation and the following rules to solve for the derivative:
Derivative of an exponential function with base other than e:
[tex]\frac{dy}{dx} a^{u} = a^{u} * u' * lna[/tex]
Power rule:
[tex]\frac{dy}{dx} x^{n} = nx^{(n-1)}[/tex]
Find the derivatives using the power rule and derivative of an exponential function. Plug these into the product rule equation:
[tex]\frac{dy}{dx} = x(3^{(2x^{2} -1)} * 4x* ln3) + (1)3^{(2x^{2} - 1)}[/tex]
Simplify by factoring out a common factor: [tex]3^{(2x^{2} - 1)}[/tex]
[tex]\frac{dy}{dx} = 3^{(2x^{2} - 1)}( x* 4x * ln3) + (1)[/tex]
Simplify further:
[tex]\frac{dy}{dx} = 3^{(2x^{2} - 1)} (4x^{2}ln3 + 1)[/tex]
This is the final derivative.
Answer:
[tex]3^{2x^2-1}+4ln(3)*3^{2x^2-1}x^2[/tex]
Step-by-step explanation:
[tex]x3^{(2x^2-1)}[/tex]
~Apply product rules
[tex]\frac{d}{dx}(x)3^{2x^2-1}+\frac{d}{dx}(3x^{2x^2-1})x\\\frac{d}{dx}=1\\(3^{2x^2-1})=4ln(3)*3x^{2x^2-1}x\\1*3^{2x^2-1}+4ln(3)*3^{2x^2-1}xx[/tex]
~Simplify
[tex]3^{2x^2-1}+4ln(3)*3^{2x^2-1}x^2[/tex]
Best of Luck!
What are the points of the inverse graph of the graph listed below
Answer:
5 and -1.5 i believe
Step-by-step explanation:
What is the translation of the point to its image? A (−1, 4)→ A' (3, 3)
Answer:
We validate that the formula to determine the translation of the point to its image will be:
A (x, y) → A' (x+4, y-1)
Step-by-step explanation:
Given
A (−1, 4)→ A' (3, 3)
Here:
A(-1, 4) is the original pointA'(3, 3) is the image of AWe need to determine which translation operation brings the coordinates of the image A'(3, 3).
If we closely observe the coordinates of the image A' (3, 3), it is clear the image coordinates can be determined by adding 4 units to the x-coordinate and subtracting 1 unit to the y-coordinate.
Thue, the rule of the translation will be:
A(x, y) → A' (x+4, y-1)
Let us check whether this translation rule validates the image coordinates.
A (x, y) → A' (x+4, y-1)
Given that A(-1, 4), so
A (-1, 4) → A' (-1+4, 4-1) = A' (3, 3)
Therefore, we validate that the formula to determine the translation of the point to its image will be:
A (x, y) → A' (x+4, y-1)
Directions - Graph the following slope intercept equation:
Answer:
?
Step-by-step explanation:
Nick has $60 in a savings account that earns 5% interest per year. How much interest will he have in 1 year?
Pls help
A.
B.
C.
D.
Answer:
The answer is A so put it
What is the reciprocal of 4? Enter your answer in the space below, using a slash mark (/) as a fraction bar when needed.
Answer:
1/4. or 0.25 :))
Step-by-step explanation:
4 as a fraction is 4/1, so the reciprocal is 1/4 :)
There are 2 mixtures of light purple paint.
Mixture A is made with 5 cups of purple paint and 2 cups of white paint.
Mixture B is made with 15 cups of purple paint and 8 cups of white paint.
Which mixture is a lighter shade of purple?
A or B
Answer:
a
Step-by-step explanation:
(10 points) only answer section b plz
If 14 gallon of paint covers 13 of a wall in Luna's bedroom, how much paint does she need to cover 1 wall?
Answer:
182
Step-by-step explanation:
1/13=14 gal
14 times 13 = 182 gal.
Unless you wrote it diff, then it would be 14/13 = 1.08 gal (I don't think this one is correct though)
Answer:
182
Step-by-step explanation:
What is the distance between the points (-2, 4) and (7, -5)?
What is the y-intercept of the function?
Answer:
-5
Step-by-step explanation:
HEPPPPPPPPPPPPPP MEEEEEEEEE
I NEED THE CORRECT ANSWER IN ORDER TO PASS PLS HELP!
Write an equation for the following problem and Solve it.
A taxi cab in Myrtle Beach charges $2 per mile and $1 for every person. If a taxi cab ride for two people costs $12, how far did the taxi cab travel?
Answer:
i believe 5 miles
Step-by-step explanation:
$12 - $2 (for the two people in the taxi cab since it costs $1 every person)
= $10
then to find out the number of miles they traveled since it costs $2 you can divide 10 by 2 and get 5 which means they traveled 5 mes
Answer:
with two people and $12, the cab will travel 5 miles
Step-by-step explanation:
equation:
2x + y = 12
x - total distance
y - # of people
12 - total cost
2x + 2 = 12
x = 5 miles
Identify the angle pair from the diagram above: <2 and <7
Answer:
2 and 7 are alternate exterior anglesStep-by-step explanation:
Alternate exterior angles are angles that are on different sides of the transversal and on the outside of the parallel lines. There is a theorem that says that alternate exterior angles are congruent if two parallel lines are cut by a transversal.
Help me on this question
Answer:
what's your questions
Bill averages 10 points a game and has 110 points for the season. Aaron averages 12 points a game and has 96 points for the season. Solve an equation to find how many games it will take until they tie in points scored if they continue at the same rate.
Answer:
ok yes
Step-by-step explanation:
The number of games it will take until they tie in points scored if they continue at the same rate is;
7 games.
We are told that Bill averages 10 points a game and has 110 points for the season.
Thus, number of games a season it will take bill to reach 110 points is; 110/10 = 11 games
Aaron averages 12 points per game and has 96 points for the season. Thus, number of games a season it will take bill to reach 96 points is;
96/12 = 8 games.
Now, let the additional number of games to be played for them to have the same points be x. Thus;
110 + 10x = 96 + 12x
12x - 10x = 110 - 96
2x = 14
x = 14/2
x = 7
In conclusion, the additional number of games it will take for Bill and Aaron to have the same number of points is 7 games.
Read more at; https://brainly.com/question/2996032
I need help with this question. Thank you so much!
Answer:
D. -5
Step-by-step explanation:
Solve 8 = x2 + 8x + 25 by completing the square.
Answer:
x = 4 ± 3i
I calculated it and I check my answer on a website. Enjoy!
WHAT IS THE RATE OF CHANGE HELP!!
Answer:
B) Y=85x
Step-by-step explanation:
The actual rate of change is 75 so you need to find which one(s) have a greater one. The other 2 that are equations have a less rate of change so it is B.
Hope this helps. Pls give brainliest.
Find the value of x and y.
Answer:x=
14 y=12
Step-by-step explanation:
What is the irs ? In math
Answer: What is the IRS's math error authority? Congress has granted the IRS “math error authority,” which allows the IRS to make certain summary adjustments to a taxpayer's return. If the changes lead to a greater amount of tax, the IRS would make an assessment.
Solve for z: 4 (z+6) -11 = 25
I need to show my work
Answer:
z=3
Step-by-step explanation:
4(z+6)-11=25
add 11 to both sides
4(z+6)-11+11=25+11
simplify
4(z+6)=36
divide each side by 4
(4(z+6))/4=36/4
Simplify
z+6=9
subtract 6 from each side
z+6-6=9-6
simplify
z=3
Answer:
z=3; plug the equation into a calculator
Simplify all four questions correctly-
(p - 3) + (p - 7)
(3n - 1) + ( -n + 4)
(-t + 5) + (3t + 2)
(7k + 9) + (4k - 3)
Answer:
1. 2p - 10
2. 2n + 3
3. 2t + 7
4. 11k + 6
Step-by-step explanation:
(-5,-3) (5,-4) slope =
Answer:
Your slope would be -1/10
Step-by-step explanation:
To find the slope from two points, you would use the formula y2-y1/x2-x1
In this case, the equation would look like -4-(-3)/5-(-5)
-4 - (-3) = -1
5 - (-5) = 10
-1/10 = -1/10
PLS HELP ME!!!!! IT IS TIMED
Answer:
C. 13
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Please answer correctly. I will give you the brainliest and 15 points!!! plzzzzzzzzzzzzz need ASAP
Which of these is not a possible r-value?
Answer:
D
Step-by-step explanation:
A value of greater than 1 is not a possible value of r or the correlation coefficient in statistics. Therefore, it is not D
Solve for x plz help!!
4(6x-9.5)=46
:) Thanks to all the people that help me out
Answer:
x = 3.5
Step-by-step explanation:
Distribute the 4
24x - 38 = 46
Add 38 to both sides
24x = 84
divide by 24
x = 3.5 or 7/2
Answer:
x=7/2
Step-by-step explanation:
A leather jacket is listed at $230 the discount rate is 25% off the list price what is the sales price of the jacket?
Answer:
Discount selling price= $172.5
Step-by-step explanation:
Giving the following information:
Selling price= $230
Discount rate= 25%
To calculate the discount selling price, we need to use the following formula:
Discount selling price= selling price*(1 - discount rate)
Discount selling price= 230* (1-0.25)
Discount selling price= $172.5
thanks for helping with the last one....a few more please help
Who's is the faster runner? Raj can run 1 1/3 laps in 1/4 of an hour. Yvonne can run 4 1/2 laps in 7/8 of an hour.
