ANSWER
(a+b)(a^2+ab+b^2)=(3x+4y) 9x^2+12xy+16y^2)
Someone help me please
Answer:
31 m
Step-by-step explanation:
v=l*w*h since it is a cube then all sides (a) are equal:
v=(a*a*a)=a^3
v1+v2=1331 for the first two boxes(
a³+a³=∛1331
l=w=h=11*2=22
v=729 ( for the second cube)
a=∛729=9
9+22=31 m
THe graph is going further than the outline ben 10 benden
Answer:
EB = 9
Step-by-step explanation:
CD = AB
The line with the value of five that also forms a right angle with EB is a perpendicular bisector to AB.
So the value of EB is half of AB (AB is equal to CD).
18/2 = 9
how do you graph X+2y=6
Answer:
x + 2y = 6
2y = -x + 6
y = -1/2x + 3
So, you will have a downward sloping, less steep line with an intercept at (0, 3).
You can use the Math is Fun Function Grapher and Calculator to graph the line.
Hope this helps!
I need answers for 1 , 2, 4
Answer:
(3) x ≥ -3
(4) 2.5 gallons
(4) -12x + 36
Step-by-step explanation:
Hey there!
1)
Well its a solid dot meaning it will be equal to.
So we can cross out 1 and 2.
And it's going to the right meaning x is greater than or equal to -3.
(3) x ≥ -3
2)
Well if each milk container has 1 quart then there is 10 quarts.
And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.
(4) 2.5 gallons
4)
16 - 4(3x - 5)
16 - 12x + 20
-12x + 36
(4) -12x + 36
Hope this helps :)
what is the answer to the equation? plz help 3x+8=9+3x-14
Answer:
It does not have an answer as 3x != 3x + 13 or not equalivalent
Step-by-step explanation:
Answer:
no solution
Step-by-step explanation:
3x+8=9+3x-14
Combine like terms
3x+8 = 3x -5
Subtract 3x from each side
8 = -5
This is never true so there is no solution
3. What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. (4 points)
Answer:
7.81
Step-by-step explanation:
its a triangular shape
let x = 4 + 2 = 6
let y = 5
length between two points = h
h² = x² + y²
h² = 6² + 5²
h = sqrt of 61
h = 7.81
Which expression is equivalent to x^-5/3?
Answer:
[tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]
Step-by-step explanation:
[tex]x^{-\frac{5}{3} }[/tex] = [tex](\sqrt[3]{x} )^{-5}[/tex] = [tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]
Which point is a solution to the inequality shown in this graph?
Answer: A, (0, -3)
Step-by-step explanation:
Inequalities, once graphed, take the form of the image you attached:
Linear inequalities are straight lines, sometimes dotted and sometimes solid, with shading on one side of the line.
Any point in the shading is a correct solution to the inequality.
When the line is solid, any point on the line is a solution to the inequality.When the line is dotted, only the shaded area past the line includes solutions - points on the line are not solutions.In this case, the line is solid, so any point on the line is a solution to the inequality.
Looking at answer choice A: (0, -3), it lies on the line as the y-intercept.
The correct choice is A.
A drawer is filled with 3 black shirts, 8 white shirts, and 4 gray shirts. One shirt is chosen at random from the drawer. Find the probability that it is not a white shirt. Write your answer as a fraction.
The probability that the shirt that is chosen at random from the drawer is not a white shirt, can be found to be 47 %
How to find the probability ?The probability that the shirt picked is not a white shirt can be found by first finding the number of shirts that are not white shorts in the drawer. This number is :
= Number of black shirts + Gray shirts
= 3 + 4
= 7 shirts
Then, find the total number of shirts in the drawer, including the white shirts :
= Number of black shirts + Gray shirts + White shirts
= 3 + 8 + 4
= 15 shirts
The probability that when a shirt is chosen at random, that it is not a white shirt is :
= Number of shirts that are not white / Total number of shirts
= 7 / 15
= 47 %
Find out more on probability at https://brainly.com/question/27831410
#SPJ1
The function y=−16x2+v0x models the height of a football in feet x seconds after a player kicks it. In the equation of the function, v0 is the ball's initial velocity in feet per second. The ball hits the ground 2 seconds after the player kicks it.
What is the value of v0?
Answer:
[tex]\large \boxed{\sf \ \ v_0=32 \ \ }[/tex]
Step-by-step explanation:
Hello,
The equation is
[tex]y=f(x)=-16x^2+v_0 \cdot x[/tex]
The ball hits the ground 2 seconds after the player kicks it, it means that f(2)=0.
We need to find [tex]v_0[/tex] such that f(2)=0.
[tex]f(2)=-16\cdot 2^2+v_0 \cdot 2=-64+2v_0=0\\\\\text{*** add 64 to both sides ***}\\\\2v_0=64\\\\\text{*** divide by 2 both sides ***} \\\\v_0=\dfrac{64}{2}=32[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
v0 = 32 ft/s
Step-by-step explanation:
Dan's mean average on 5 exams is 86 determine the sum of his score
Answer: 430
Step-by-step explanation:
An average of 5 scores can be found via: (the sum of the scores)*5. Thus, simply multiply 86*5 to get that the sum of his scores is 430
Hope it helps <3
The graph of an absolute value function has a vertex of (2,3) and crosses the x-axis at (−1,0) and (5,0). What is the equation for this absolute value function when y=0? A 0=|x+2|+3 B 0=|x−2|+3 C 0=−|x+2|+3 D 0=−|x−2|+3
Answer:
Option D.
Step-by-step explanation:
The vertex form of an absolute function is
[tex]y=a|x-h|+k[/tex]
where, a is a constant, (h,k) is vertex.
It is given that, vertex of an absolute function is (2,3). So, h=2 and k=3.
[tex]y=a|x-2|+3[/tex] ...(1)
It crosses the x-axis at (5,0). So put x=5 and y=0 to find the value of a.
[tex]0=a|5-2|+3[/tex]
[tex]-3=3a[/tex]
[tex]-1=a[/tex]
Put a=-1 in (1).
[tex]y=(-1)|x-2|+3[/tex]
[tex]y=-|x-2|+3[/tex]
Now, put y=0, to find the equation for this absolute value function when y=0.
[tex]0=-|x-2|+3[/tex]
Therefore, the correct option is D.
Answer:
I got this question on my test and I answered D cause if you look up the graph it matches the question
Step-by-step explanation:
D 0=−|x−2|+3
A 24-centimeter by 119-centimeter piece of cardboard is used to make an open-top box by removing a square from each corner of the cardboard and folding up the flaps on each side. What size square should be cut from each corner to get a box with the maximum volume
Answer:
The size square removed from each corner = 32.15 cm²
Step-by-step explanation:
The volume of the box = Length * Breadth * Height
Let r be the size removed from each corner
Note that at maximum volume, [tex]\frac{dV}{dr} = 0[/tex]
The original length of the cardboard is 119 cm, if you remove a size of r (This typically will be the height of the box) from the corner, since there are two corners corresponding to the length of the box, the length of the box will be:
Length, L = 119 - 2r
Similarly for the breadth, B = 24 - 2r
And the height as stated earlier, H = r
Volume, V = L*B*H
V = (119-2r)(24-2r)r
V = r(2856 - 238r - 48r + 4r²)
V = 4r³ - 286r² + 2856r
At maximum volume dV/dr = 0
dV/dr = 12r² - 572r + 2856
12r² - 572r + 2856 = 0
By solving the quadratic equation above for the value of r:
r = 5.67 or 42
r cannot be 42 because the size removed from the corner of the cardboard cannot be more than the width of the cardboard.
Note that the area of a square is r²
Therefore, the size square removed from each corner = 5.67² = 32.15 cm²
Translate this sentence into an equation. 59 is the sum of 11 and Mai’s score
Answer:
11 + Mai's Score = 59
Step-by-step explanation:
You need to add 11 and Mai's score together to get 59, so with the values given we can make the equation 11 + Mai's Score = 59.
*depending on the question, Mai's score may need to be said as a letter variable, so:
If m = mai's score,
11 + m = 59
I hope this helped! :)
the perimeter of a square flower bed is 100 feet. what is the area of the flower bed in sqaure feet
Answer:
A =625 ft^2
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
100 =4s
Divide each side by 4
100/4 = 4s/4
25 = s
A = s^2 for a square
A = 25^2
A =625
a.
C.
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range-
y = -5x² - 4x + 1
D: all real numbers
D: (x20)
R: ( 31.8)
R: all real numbers
b. D: all real numbers
d. D: all real numbers
R: ( 2 1.8)
R: ( 30.2)
Answer:
Step-by-step explanation:
y = -5x² - 4x + 1 is a quadratic and thus is defined on the domain "all real numbers." Because of the negative sign in front of the x^2 term, we know that this parabolic curve opens downward. The x-coordinate of the vertex is x = -b/[2a], which in this case is x = 4/[2*-5], or -4/10, or -2/5. Using synthetic division to determine the y-coordinate of the vertex, we get vertex (-2/5, 9/5). 9/5 is the maximum y value. The range is (-infinity, 9/5].
I need help I just don't understand
Answer: 9/7 or -5/2
Step-by-step explanation:
We can only factorise quadratics if they're in the format ax^2 + bx + c
Re-arranging the equation gives 14x^2 + 17x - 45 = 0
Factorising this quadratic gives:
(7x - 9)(2x + 5) = 0
There are numerous ways to factorise quadratics, using a calculator or via alternate methods you may have learnt in class. (E.g. 2 numbers multiply to make (14 * -45) and add up to make (17).
This gives us our solutions.
x = 9/7 or x = -5/2
Answer:
See below.
Step-by-step explanation:
First, move all the terms to one side so we have only a zero on the right:
[tex]6x^2-17x+13=20x^2-32\\-14x^2-17x+45=0\\14x^2+17x-45=0[/tex]
(I divided everything by negative 1 in the third step. This is optional, but I like having the first term positive.)
Now, we just need to factor it. To factor, what you want to do is find two numbers a and b such that:
When a and b is multiplied together, they equal the first coefficient and constant multiplied together.
And when a and b is added together, they equal the second term.
In other words, we want to find two numbers that when multiplied equals 14(-45)=-630 and when added equals 17. Then, we can substitute this into the 17. You do this by guessing and checking. It's useful to have a calculator.
After a bit, you can find that 35 and -18 works. Thus:
[tex]14x^2+17x-45=0\\14x^2+35x-18x-45=0\\7x(2x+5)-9(2x+5)=0\\(7x-9)(2x+5)=0[/tex]
Now, the finish the problem, we just need to use the Zero Product Property and solve for x:
[tex]2x+5=0\\x=-5/2\\\\7x-9=0\\x=9/7[/tex]
Note: This only works for quadratics.
n = 9
H0 : 50 = 47
Ha : 50 s = 3
Assume data are from normal population. The p-value is equal to:______.
a. 0.0171.
b. 0.0805.
c. 0.2705.
d. 0.2304.
Answer:
The p-value is 0.809.
Step-by-step explanation:
In this case we need to perform a significance test for the standard deviation.
The hypothesis is defined as follows:
H₀: σ₀ = 4 vs. Hₐ: σ₀ ≤ 4
The information provided is:
n = 9
s = 3
Compute the Chi-square test statistic as follows:
[tex]\chi^{2}=\frac{(n-1)s^{2}}{\sigma_{0}^{2}}[/tex]
[tex]=\frac{(9-1)\cdot (3)^{2}}{(4)^{2}}\\\\=\frac{8\times 9}{16}\\\\=4.5[/tex]
The test statistic value is 4.5.
The degrees of freedom is:
df = n - 1
= 9 - 1
= 8
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{9}>4.5)=0.809[/tex]
*Use a Chi-square table.
Thus, the p-value is 0.809.
A poll reported that 66 percent of adults were satisfied woth the job the major airlines were doing. Suppose 25 adults are selected at random and the number who are satisfied is recorded.
1. Explain why this is a binomial experiment.
A. This is a binomial experiment because there are three mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
B. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a random number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
C. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success changes in each trial.
D. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
2) Find and interpret the probability that exactly 15 of them are satisfied with the airlines.
Answer:
A)Option D
B)P(X = 15) = 0.1325
Step-by-step explanation:
A) From the question, the information given follows binomial distribution because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials. The outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
So option D is correct.
B) From the question, we are told that the poll reported that 66 percent of adults were satisfied with the job. Thus, probability is; p = 0.66
Let X be the number of adults satisfied with the job. Since 25 are selected,
Thus;
P(X = 15) = C(25, 15) * (0.66)^(15) * (1 - 0.66)^(25 - 15)
P(X = 15) = 3268760 × 0.00196407937 × 0.00002064378
P(X = 15) = 0.1325
There will be a circular patio with a diameter of 7 metres. Greg is going to put a tiled edge around the patio. What is the circumference of the patio? m Circumference of a circle = 2πr Use π = 3.14
Answer:
[tex]Circumference = 21.99 \ m[/tex]
Step-by-step explanation:
Circumference = [tex]\pi d[/tex]
Given that d = 7 m
[tex]Circumference = (3.14)(7)\\[/tex]
[tex]Circumference = 21.99 \ m[/tex]
Answer:
[tex]\boxed{21.98 \: \mathrm{meters}}[/tex]
Step-by-step explanation:
Apply formula for circumference of a circle.
[tex]C=\pi d[/tex]
[tex]d:diameter[/tex]
Take [tex]\pi =3.14[/tex]
Plug [tex]d=7[/tex]
[tex]C=3.14 \times 7[/tex]
[tex]C= 21.98[/tex]
You change oil every 6000 miles and drive 2000 miles a month; how many times a year do you change oil?
Answer:
you would change it 4 times a year
Step-by-step explanation:
if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4
the solution of the equation 0=4+4(m+1) is
Answer:
[tex]\boxed{m = -2}[/tex]
Step-by-step explanation:
[tex]0 = 4+4(m+1)[/tex]
Resolving Parenthesis
[tex]0 = 4+4m + 4[/tex]
[tex]0 = 4m+8[/tex]
Subtracting 8 to both sides
[tex]-8 = 4m[/tex]
[tex]4m = -8[/tex]
Dividing both sides by 4
m = -8/4
m = -2
Step-by-step explanation:
4+4m+4= 0
4m+8=0
4m=-8
m= -8/4=-2
WILL MARK BRAINLIST----- A particular map shows a scale of 1 cm:5 km. What would the map distance be (in cm) if the actual distance to be represented is 14 km?
Answer:
2.8 cm
Step-by-step explanation:
The map scale is 1 cm : 5 km. That means that 1 cm is equal to 5 km.
To find the map distance (in cm), we have to set up a ratio.
[tex]\frac{1 cm}{5 km} = \frac{x}{14 km}[/tex]
X (the map distance in cm) is over the actual distance of 14 km.
Now cross multiply and divide.
[tex]5x = 14[/tex]
[tex]\frac{5x}{5} = \frac{14}{5}[/tex]
[tex]x = 2.8 cm[/tex]
If the actual distance to be represented is 14 km, the map distance (in cm) will be 2.8 cm.
Hope that helps.
What is 7/8×3/9 reduced to lowest terms
Answer:
7/24
Step-by-step explanation:
7/8×3/8= 21/72
divide using 3
= 7/24
EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k. SOLUTION (a) The gradient of f is ∇f(x, y, z) = fx(x, y, z), fy(x, y, z), fz(x, y, z)
Answer:
a) f = sin(yz)i + xzcos(yz)j + xycos(yz)kb) -2Step-by-step explanation:
Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;
fx, fy and fz are the differential of the functions with respect to x, y and z respectively.
a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k
The gradient of f = sin(yz)i + xzcos(yz)j + xycos(yz)k
b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v
∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k
∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k
∇f(1, 2, 0) = 0i +0j + 2k
Given v = i + 4j − k
∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)
∇f(1, 2, 0)*v = (0i +0j + 2k)*(i + 4j − k )
Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0
∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k
∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)
∇f(1, 2, 0)*v =0+0-2
∇f(1, 2, 0)*v= -2
Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2
please show on graph (with x and y coordinates) state where the function x^4-36x^2 is non-negative, increasing, concave up
Answer:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
Step-by-step explanation:
For this case we have the following function:
[tex] y= x^4 -36x^2[/tex]
We can find the first derivate and we got:
[tex] y' = 4x^3 -72x[/tex]
In order to find the concavity we can find the second derivate and we got:
[tex] y'' = 12x^2 -72[/tex]
We can set up this derivate equal to 0 and we got:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
A landscaping company charges $50 per cubic yard of mulch plus a delivery charge of $24. Find a
linear function which computes the total cost C(in dollars) to deliver a cubic yards of mulch.
C(x) =
Answer: c(x) = $50*x + $24
Step-by-step explanation:
First, this situation can be modeled with a linear equation like:
c(x) = s*x + b
where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)
Then we know that:
The company charges $50 per cubic yard, so the slope is $50
A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.
Then our equation is:
c(x) = $50*x + $24
This is:
"The cost of buying x cubic yards of mulch"
Which of the following statements is correct about quadratic number patterns? A. The third difference is greater than zero. B. The first difference is constant. C. The difference between terms is always positive. D. The second difference is constant.
Answer: D.) The second difference is constant.
Step-by-step explanation:
The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant.
Answer:
D.
Step-by-step explanation:
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k. A) 2 B) 3 C) 4 D) 5 IF YOU ANSWER IN 5 MINUTES I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!
Ans k = 4
Step-by-step explanation:
Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and
f(x) = [tex]\frac{-1}{3} x -3[/tex]
Now, g(x) = f(x) + k
or, [tex]\frac{-1}{3}x + 1[/tex] = [tex]\frac{-1}{3} x -3 + k[/tex]
or, 1 + 3 = k
So, k = 4 Answer.
Differentiate with respect to x and simplify your answer. Show all the appropriate steps? 1.e^-2xlog(ln x)^3 2.e^-2x(log(ln x))^3 3.sin(xe^x)^3 4.sin^3(xe^x) 5.ln(xy)=e^2y
(1) I assume "log" on its own refers to the base-10 logarithm.
[tex]\left(e^{-2x}\log(\ln x)^3\right)'=\left(e^{-2x}\right)'\log(\ln x)^3+e^{-2x}\left(\log(\ln x)^3\right)'[/tex]
[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{e^{-2x}}{\ln10(\ln x)^3}\left((\ln x)^3\right)'[/tex]
[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}(\ln x)^2}{\ln10(\ln x)^3}\left(\ln x\right)'[/tex]
[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}(\ln x)^2}{\ln10\,x(\ln x)^3}[/tex]
[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}}{\ln10\,x\ln x}[/tex]
Note that writing [tex]\log(\ln x)^3=3\log(\ln x)[/tex] is one way to avoid using the power rule.
(2)
[tex]\left(e^{-2x}(\log(\ln x))^3\right)'=(e^{-2x})'(\log(\ln x))^3+e^{-2x}\left(\log(\ln x))^3\right)'[/tex]
[tex]=-2e^{-2x}(\log(\ln x))^3+3e^{-2x}(\log(\ln x))^2(\log(\ln x))'[/tex]
[tex]=-2e^{-2x}(\log(\ln x))^3+3e^{-2x}(\log(\ln x))^2\dfrac{(\ln x)'}{\ln10\,\ln x}[/tex]
[tex]=-2e^{-2x}(\log(\ln x))^3+\dfrac{3e^{-2x}(\log(\ln x))^2}{\ln10\,x\ln x}[/tex]
(3)
[tex]\left(\sin(xe^x)^3\right)'=\left(\sin(x^3e^{3x})\right)'=\cos(x^3e^{3x}(x^3e^{3x})'[/tex]
[tex]=\cos(x^3e^{3x})((x^3)'e^{3x}+x^3(e^{3x})')[/tex]
[tex]=\cos(x^3e^{3x})(3x^2e^{3x}+3x^3e^{3x})[/tex]
[tex]=3x^2e^{3x}(1+x)\cos(x^3e^{3x})[/tex]
(4)
[tex]\left(\sin^3(xe^x)\right)'=3\sin^2(xe^x)\left(\sin(xe^x)\right)'[/tex]
[tex]=3\sin^2(xe^x)\cos(xe^x)(xe^x)'[/tex]
[tex]=3\sin^2(xe^x)\cos(xe^x)(x'e^x+x(e^x)')[/tex]
[tex]=3\sin^2(xe^x)\cos(xe^x)(e^x+xe^x)[/tex]
[tex]=3e^x(1+x)\sin^2(xe^x)\cos(xe^x)[/tex]
(5) Use implicit differentiation here.
[tex](\ln(xy))'=(e^{2y})'[/tex]
[tex]\dfrac{(xy)'}{xy}=2e^{2y}y'[/tex]
[tex]\dfrac{x'y+xy'}{xy}=2e^{2y}y'[/tex]
[tex]y+xy'=2xye^{2y}y'[/tex]
[tex]y=(2xye^{2y}-x)y'[/tex]
[tex]y'=\dfrac y{2xye^{2y}-x}[/tex]