Let f(x) = -5x^6√x + -7/x³√x. What would f’(x) be? If anyone could show me step-by-step, I would greatly appreciate it! I’ve worked out this problem 4 times already and I can’t seem to get the right answer.
Answers
Answer:
[tex]f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}[/tex]
or
[tex]f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}[/tex]
Step-by-step explanation:
Rather than solving this question in a more complex method by directly using the product rule and quotient rule, it can first be considered to perform some algebraic manipulation (index laws) to simplify the expression before taking the derivative.
[tex]\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^6\ \sqrt{x}\ +\ \frac{-7}{x^3\ \sqrt{x}}\\\\f\left(x\right)\ =\ -5x^6\cdot x^{\frac{1}{2}}\ +\ \frac{-7}{x^3\cdot x^{\frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{6\ +\ \frac{1}{2}}\ +\ \frac{-7}{x^{3\ +\ \frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ +\ \frac{-7}{x^{\frac{7}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\end{array}[/tex]
Now, the derivative of the function can be calculated simply by only using the power rule, which yields
[tex]\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\\\\f^{\prime}\left(x\right)\ =\ \left(-5\right)\left(\frac{13}{2}\right)\left(x^{\frac{13}{2}\ -\ 1}\right)\ -\ \left(7\right)\left(-\frac{7}{2}\right)\left(x^{-\frac{7}{2}\ -\ 1}\right)\\\\f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}\\\\f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}\end{array}\\\end{large}[/tex]
Related Questions
X+24=35 how to solve this
Answers
Answer:
X = 11
Step-by-step explanation:
Simplifying
X + 24 = 35
Reorder the terms:
24 + X = 35
Solving
24 + X = 35
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-24' to each side of the equation.
24 + -24 + X = 35 + -24
Combine like terms: 24 + -24 = 0
0 + X = 35 + -24
X = 35 + -24
Combine like terms: 35 + -24 = 11
X = 11
Simplifying
X = 11
Answer:
x+24=35
then collect like terms together, which means "x" terms in one side and numbers in one side:
x=35-(+24)
we need to change the signs when ever we change its place, like changing from one side to another
x=35-24
x=11. ✓
There are two boxes of cereal in the shape of rectangular prisms on a shelf. The
dimensions of each box of cereal are listed below.
. Box B has a height of 25 centimeters, a length of 19 centimeters,
and a width of 6 centimeters.
• Box A has a height of 25 centimeters, a length of 20 centimeters,
and a width of 9 centimeters.
What is the difference in volume, in cubic centimeters, between the two boxes of cereal?
A 1,650
B 3,900
C 4,500
D 7,350
Answers
Answer:
1650 Cubic Centimeters
Step-by-step explanation:
To get the volume of the cereal boxes, you must multiply their 3 dimensions together.
Box A:
25×20=500
500×9=4500
Box B:
25×19=475
475×6=2850
Now, to find the difference of these volumes, you want to subtract the smaller volume from the larger volume.
4500-2850=1650
The answer is 1650 cubic centimeters.
Describe a scenario where the function value exists at x=c, but the limit does not exist.
Answers
The scenario can be described using a piecewise function like:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
When the value exists but the limit does not?
Remember that the limit only exists if the limit from left and the limit from the right give the same value.
Then, we can just define a piecewise function of the form:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
Clearly, this is not a continuous function.
Notice that:
[tex]f(c) = c.\\\\ \lim_{x \to c^{-}} f(x) = 1/c\\\\ \lim_{x \to c^{+}} f(x) = 1/(c + 73)[/tex]
So the limits from left and right are different, then:
[tex]\lim_{x \to c^{}} f(x)[/tex]
Does not exist.
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How much for $100 invested in 6% interest compounded monthly be worse after 20 years
Answers
Answer:
$331.02
Step-by-step explanation:
compound interest formula
A = P ( 1 + r/n)^nt
P = principal amount
r = rate decimal
n = number of times interest is compounded
t = time
A = 100 * (1 + .06/12)^(12*20)
A = 331.02
1. Draw an appropriate Venn diagram to depict each of the following sets. U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbers. 1. Draw an appropriate Venn diagram to depict each of the following sets . U = The set of integers . A = The set of even integers . B = The set of odd integers . C = The set of multiples of 3 . D= The set of prime numbers .
Answers
The attached diagram represents the Venn diagram of the sets
How to draw the Venn diagram?The sets are given as:
The universal set, U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbersFrom the above representation, we have the following highlights:
Set A and set B will not intersect, because no number can be even and oddSet C and set D will intersect set A because they have common elements 6 and 2, respectivelySet C and set D will intersect set B because they have common elements 3 and 3, respectivelyUsing the above highlights, we can now draw the Venn diagram
See attachment for the Venn diagram
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An empty rectangular tank was 25 cm long, 23 cm wide and 18 cm high. Ravi filled 5 identical bottles with water to the brim. Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle? height of water, = = 1/2 X 18 3 23 cm Co 25 cm 3 full. 18 cm 2 An empty rectangular tank was 25 cm long , 23 cm wide and 18 cm high . Ravi filled 5 identical bottles with water to the brim . Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle ? height of water , = = 1/2 X 18 3 23 cm Co 25 cm 3 full . 18 cm
Answers
What is the multiplicative rate of change between 10,50 and 250
Answers
Answer:D
Step-by-step explanation:
Sianna bought 3 pens, 4 notebooks, and a calculator. The calculator cost $25. If x represents the cost of each pen and y represents the cost of each notebook, which expression represents the amount of change Sianna should receive from $50?
3x + 4y +25
50 – (3x + 4y)
50 – (3x + 4y + 25)
3x + 4y + 25 + 50
Answers
Answer:
50 – (3x + 4y + 25)
Step-by-step explanation:
To see how much change she is gonna receive we need to find how much she spent on the items and add them all up:
The calculator was $25
The price of pens and notebooks are unknown so they are represented with x and y respectively.
With given information we can write the following equation to see the change she will receive:
50 – (3x + 4y + 25)
Mirele needs to buy fencing to completely surround her backyard pool. How much fencing should she buy?
A pool has a length of 31.74 feet and a height of 14.85 feet.
Answers
Answer:
93.18 feet
Step-by-step explanation:
Length of backyard pool = 31.74 feet
Height of backyard pool = 14.85 feet
To find = Use the formula for the perimeter of a rectangular pool.
= 2 ( length + height )
Length of fencing bought by Mirele:
2 ( 31.74 + 14.85 ) = 2 ( 46.59 ) = 93.18 feet
SUPER URGENT AND EASY FOR MOST- 30 PTS
factorise
10x + 300
Answers
Answer:
10(x + 30)
Step-by-step explanation:
10x + 300
Both terms have 10 in common, so you can factor out 10.
10x + 300 = 10(x + 30)
what is the probability that s+d>3 and s.d>3? write your answer as a decimal rounded to hundreth place
Answers
The probability that s+d > 3 and sd > 3 is 0.03.
SolutionPlot the inequalities
The region -5 ≤ s,d ≤ 5 is the square shaded in grey.
The region s + d > 3 is the region Q shaded to the right of the straight line.
The region sd > 3 is the region R shaded to the right of the curve d = 3/s.
Find the intersection of the three regions
From the figure, the region satisfying all the above three inequalities is the region to the left of the curve d = 3/s, bounded by the square region, i.e. the region R.
Probability of region R
The required probability is the Geometric probability of the intersection region R. It is calculated as
P(R) = ar(region R) / ar(square region P).
Calculate the areas of the regions
ar(region R) = area of the rectangle to the right in the first quadrant formed by dropping a vertical from point F - area under the curve d = 3/s in the first quadrant
[tex]\[\Rightarrow \;\; \mathrm{ar(\mathbf{R}) =} \int_{3/5}^5\frac{3}{s}ds = 25-3-3\ln\frac{25}{3} = 15.64.\][/tex]
ar(region P) = 25 × 25 = 625.
Calculate P(R)
The probability of the region R, P(R) = 15.64 / 625 = 0.025.
Rounding it to the hundredth place of decimal, P(R) = 0.03.
The probability that s+d >3 and sd>3, where -5 < s,d < 5, is 0.03.
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Disclaimer: The question was incomplete. Please find the full content below.
What is the probability that s + d > 3 and sd > 3, where -5 ≤ s,d ≤5? Write your answer as a decimal rounded to the hundredth place.
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please help! write D u E and D n E using interval notation.
Answers
Part 1
[tex]D \cup E[/tex] denotes the union of the two sets (in other words, all the elements in both sets).
This means it is [tex](-\infty, 4) \cup [7, \infty)[/tex]
Part 2
[tex]D \cap E[/tex] denotes the elements shared between both sets.
This means the answer is [tex](4, 7][/tex]
A tower on a college campus was built with a faulty foundation and is starting to lean. A student climbs to the tilted top and drops a rope down to the ground. The
end of the rope lands 3 feet from the base of the tower and measures 57 feet from
the top of the building to the ground. What is the angle that the tower is leaning?
Round your answer to the nearest degree, and enter the number only
Answers
Answer:
leaning at 3 degrees off of normal (to the nearest whole degree)
Step-by-step explanation:
To visualize, let's assume the tower is leaning to the right, (as viewed by us).
If the rope is dropped from the top to the ground, the tower, the rope and the ground (between the rope and the tower) form a right triangle.
The height and base of the triangle are given
Often we're looking for the angle near the ground, but here, we're looking for the angle between the rope and the tower because the angle is congruent to the angle that the tower forms with it's original vertical position (alternate interior angles). If the tower was standing straight up and hadn't been leaning at all, we wouldn't say that the tower was leaning 90°... we would say it was leaning 0°. Whereas if the tower fell over and was laying flat on the ground, we would say it was leaning at 90°. So, we're not measuring the angle between the tower and the ground, but rather the angle between the tower where it should be, and where it is... which is the same angle as the rope forms with the tower.
Recall that [tex]tan(\theta)=\dfrac {opp}{hyp}[/tex]
Since we know the two legs of the right triangle, one can setup a tangent relationship with the two legs, but remember that the "opposite" side is going to be the ground, and the "adjacent side" will be the rope.
[tex]tan(\theta)=\dfrac {ground}{rope}\\tan(\theta)=\dfrac {3ft}{57ft}\\tan(\theta)=\frac {3}{57}\\\theta=tan^{-1}(\frac {3}{57})\\\theta=3.012787504^o\\\theta \approx 3^o\\[/tex]
What is the solution to this system of equations
3x+y=17
X+2y=49
Answers
Answer:
x=−3 and y=26
Step-by-step explanation:
Let's solve your system by substitution.
3x+y=17;x+2y=49
Step: Solve 3x+y=17 for y:
3x+y=17
3x+y+−3x=17+−3x(Add -3x to both sides)
y=−3x+17
Step: Substitute−3x+17 for y in x+2y=49:
x+2y=49
x+2(−3x+17)=49
−5x+34=49(Simplify both sides of the equation)
−5x+34+−34=49+−34(Add -34 to both sides)
−5x=15
-5x/5 = 15/-5 (Divide both sides by -5)
x=−3
Step: Substitute −3 for x in y=−3x+17:
y=−3x+17
y=(−3)(−3)+17
y=26(Simplify both sides of the equation)
Answer:
x=−3 and y=26
plot the point A(-1,1) B(-3,2) and C (-1,2) in a cartesian plane name the figure so obtained by join A , B and C Also find is area
Answers
The area of the right angle triangle is 1 square unit and the figure is a right angle triangle after plotting the points on a cartesian plane.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have three point A(-1,1) B(-3,2) and C (-1,2) in a cartesian plan.
After plotting the points on the cartesian plane.
We will get a right-angle triangle,
The area of the right angle triangle = (1/2)height×base
Base length from the graph = 1 units
The height of the triangle = 2 units
= (1/2)(2)(1)
= 1 square units
Thus, the area of the right angle triangle is 1 square unit and the figure is a right angle triangle after plotting the points on a cartesian plane.
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In ΔABC, m < C = 50* , a = 14 and b = 15. Find the length of side c, to the nearest integer.
Answers
The length of the side c, to the nearest integer is 12.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
u² = s² + t² - 2(s)(t)·cos U
In ΔABC, m < C = 50* , a = 14 and b = 15.
We can solve for the length of side a to the nearest whole number using the Laws of Cosines
c² = b² + a²- 2ba CosC
Solving for the value of a, we have:
c² = 15² + 14²- 2(15)(14)cos50°
c² = 225 + 196 - 269.97
c² = 151.029
c = 12.28
Hence, The length of the side c, to the nearest integer is 12.
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Large eggs weigh 1/1/2 pounds per dozen. Dawn bought eight large eggs. How much did the eggs weigh
Answers
Answer:
12
Step-by-step explanation:
1.5 is 1 1/2 in decimal form
1.5×8=12
What is the difference when estimating?
Answers
Answer:
1 1/6 = 1
5/9 = 45/99
Step-by-step explanation:
When rounding, make sure that anything that's above half will be rounded up if anything is below half it will be rounded down.
e.g. Round to the nearest half or whole
1. 5/9
Answer: 45/99
Why: 5/9 is 4 units to 9 while 5/9 is half of a unit closer to 45/99
2. 8/10
Answer: 10/10 or 1
Why: 8/10 is 2 units from 10 while 8/10 is 3 units from 5
Hopefully this helped!
Solvex + 5-6 = 7.
OA. x = -8 and x = -18
OB. x = 8 and x = -8
C. x = -8 and x = 18
OD. x = 8 and x = -18
Answers
Because 5-6=-1….. 7- -1= 8…… then it’s just that.I
I don’t understand the answers given tho but that’s my guess
A pattern has 38 black squares to every 24 red squares. What is the ratio of black squares to red squares?
Answers
Step-by-step explanation:
the answer is 38/24 so the final answer is 19/12
Timothy is an hourly employee and he can work maximum of 40 hours in a week. If the weekly salary depends on the number of hours (h) worked, what will be the domain of the function in this context?
a. h < 40, h ∈ Z
b. h ≥ 0, h ∈ R
c. 0 ≤ h ≤ 40, h ∈ R
d. h ≤ 40, h ∈ R
Answers
Answer:
C
Step-by-step explanation:
0 ≤ h ≤ 40, h ∈ R
Hope this helps :)
The May bank statement for Rental shows a balance of $6,000, but the balance per books shows a cash balance of $8,000. Other information includes: 1. A check for $190 to pay the electric bill was recorded on the books as $10. 2. Included on the bank statement was a note collected by the bank for $450 plus interest of $30. 3. Checks outstanding totaled $270. 4. Bank service charges were $60. 5. Deposits in transit were $2,510.
Answers
The adjusted cash Balance is $8060 .
What is Bank Balance ?The amount of money in a person's account at any given time is the Bank Balance of that person's account.
Unadjusted bank balance 6000
Difference in the electricity bill -180
Add: Deposit in transit 2510
Less: Outstanding Checks -270
Adjusted cash balance 8060
So answer is a) $8060
Therefore the adjusted cash Balance is $8060 .
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write a quadratic function in standard form with zeros -5 and 0
Answers
Answer:
(x^2+5x)
Step-by-step explanation:
The inverse of the function f(x) =
f(x) = x + 10 is shown.
h(x) = 2x-0
What is the missing value?
0 1
05
O 10
O 20
Answers
Answer: 20
Step-by-step explanation:
Let [tex]f(y)=x[/tex]
[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]
solve the following inequality, algebra 1.
will give brainliest answer !!
Answers
Answer:
See below
Step-by-step explanation:
r/6 <-6 multiply both sides by 6 to get
r < - 36
or 4r+2 > 18 subtract 2 from both sides of the equation
4r > 16 divide both sides by 4
r > 4
Step-by-step explanation:
[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]
[tex]4r + 2 > 18 \: \: \: \: \: \: \: \: \: \: ...2[/tex]
Solving for inequality 1:
[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]Multiplying both sides by 6:
6 * 1/6 r < -6*6r < -36Hence the solution is r < -36
Solving for inequality 2:
4r + 2 > 18Subtract 2 from both sides:
4r + 2 - 2 > 18 - 24r > 16Divide both sides by 4:
[tex] \cfrac{4r}{4} > \cfrac{16}{4} [/tex][tex]r > 4[/tex]Hence the answer is r > 4.
The sum of the digits of a two-digit number is 14. When the digits are
reversed, the new number is 36 less than the original number. Find the
original number. Check your answer.
O The original number is 59.
O The original number is 68.
O The original number is 86.
O The original number is 95
Answers
First, lets figure out which ones add up to 14
5+9=14
6+8=14
8+6=14
9+5=14
They all add up to 14.
Next, reverse the digits and see if it is 36 less than the original number
95 is not 36 less than 59
86 is not 36 less than 68
68 is only 18 less than 86
59 is 36 less than 95
So, the answer would be 95.
Graph the linear function whose equation is y-2=-(x+1) by following these steps:
y
X
y
4
Step 1: Identify the slope.
slope = =
Answers
Answer:
slope == -1
Step-by-step explanation:
y-2 = -(x+1)
; y-2 = -x-1 expanding the bracket
; y = -x-1+2
; y = 1-x
hence slope equals -1
Help asap !………………………
Answers
Answer:
c
Step-by-step explanation:
dvdywuwhfuwi eurue wuid
What is the a-value of the graph?
Answers
What are the rational roots of ? x = 1, x = -1 x = 1, x = 0 x = 1, x = 2 This polynomial has no rational roots.
