Answer:
[tex]f'(x)=1+\ln x[/tex]
Step-by-step explanation:
[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].
Recall the product rule:
[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]
Therefore, we have:
[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]
Note that:
[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]
Simplify:
[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]
The derivative is:
[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]
[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]
[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]
[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]
[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]
[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]
MissSpanishDirections: Place the LETTER of each value in its location in the real number system below
-0.2917 rounded to the nearest hundredth.
Answer: -0.29
Step-by-step explanation:
What is the value of 20 - (3 × 23 - 5)?
A
-191
B
1
C
11
D
131
Answer:
20 - (3 × 23 - 5) = 20 - (69 - 5) =20 - 64 =- 44Note.
The answer options are not matching the question. Something is wrong with the question.
[tex]\huge\boxed{\frak{Hey\ there!}}[/tex]
[tex]\huge\boxed{\frak{20 - (3\times23-5)}}\\\\\huge\boxed{\frak{3\times23 \rightarrow 69}}\\\\\huge\boxed{\frak{= 20 - (69 - 5)}}\\\\\huge\boxed{\frak{69 - 5 \rightarrow 64}}\\\\\huge\boxed{\frak{= 20 - 64}}\\\\\huge\boxed{\rightarrow\frak{-44}}\\\\\\\boxed{\frak{Answer: -44}}\huge\checkmark\\\boxed{\rm{\star \ None\ of\ the\ above\ }\star}[/tex]
[tex]\frak{Good \ luck \ on \ your \ assignment \ and \ enjoy\ your \ day!}\\\\\\\\\frak{Amphitrite1040}[/tex]
if (a+3,b-2=b-1,2a-3 then find the value of A and B
Answer:
a=5 and b=9
Step-by-step explanation:
(x, y) = (s, t) => x=s and y=t
Hence, a+3=b-1 and b-2=2a-3, solving we get a=5 and b=9
i need help with my math please
Answer:
x is equal to 6√3
Step-by-step explanation:
[tex] - \frac{2}{3} \sqrt{5} . \: { \boxed{x}}. \: \sqrt{7} = - 4 \sqrt{105} \\ \\ - \frac{2}{3} \sqrt{5} .{ \boxed{x}}. \sqrt{7} = - 4( \sqrt{3} \times \sqrt{5} \times \sqrt{7} ) \\ \\ - \frac{2}{3} x = - 4 \sqrt{3} \\ \\ x = \frac{12 \sqrt{3} }{2} \\ \\ x = 6 \sqrt{3} [/tex]
Two rectangles are similar. The smaller has a length of 8 cm and an area of 40 cm.
If the width of the larger rectangle is 10 cm, find its area.
Answer:
160 cm²
Step-by-step explanation:
If the two rectangles are similar, that means they have equal scale factors. The smaller rectangle has length of 8 cm and area of 40 cm, which means the width is 5 cm.
The width of the larger rectangle is 10 cm, which is double the width of the smaller, similar rectangle. So, to find the length of the larger rectangle, multiply 8 x 2, which gives you 16 cm for the length, since the scale factor is 2.
Now, just find the area of the larger rectangle by doing length x width. 16cm x 10 cm = 160 cm²
Answer:
160 cm^2
Step-by-step explanation:
Our strategy is to find the length of the larger rectangle so we can find the area. To find the length, we will rely on the fact the two rectangles are "similar": their sides are in equal proportions, or have the same "ratio."
We know that the smaller rectangle has a width of 5 cm because, when we substitute area and length into
A = lw
we get
40 = 8w
w = 5
when we divide both sides by 8.
Because of equal proportions:
Width : length of the smaller rectangle = Width : length of the larger rectangle
We can write an equation
5 / 8 = 10 / x
Cross multiply
5x = 80
x = 16
So the larger rectangle has a length of 16 cm and a width of 10 cm (given)
meaning the area is
16 * 10 = 160 cm^2
Sumita is following this recipe to make flapjacks. Sumita uses 15 g of sultanas. How many flapjacks is Sumita making? Recipe: Makes 14 flapjacks 210 g margarine 150 g sugar 135 mL syrup 240 g oats 30 g sultanas
Answer:
7
Step-by-step explanation:
Sumita uses 30g sultanas for 14 so we have 30:2 =15 => 14:2=7
Solution of equation??
Answer:
[tex] \frac{3p}{5} - 15 = 3 \\ 3p - 15 = 15 \\ 3p = 15 + 15 \\ 3p = 30 \\ p = 10[/tex]
1. Give an example of a whole number that is not a natural number
2. Give an example of a rational number that is not a whole number.
3. Give an example of a real number that is irrational.
4. Are integers always/sometimes/never whole numbers?
5. Are natural numbers always/sometimes/never rational numbers?
6. Are irrational numbers always/sometimes/never rational numbers?
Glas
Answer:
2
Step-by-step explanation:
With 4 weeks remaining in the season, Lisa has 31 more homeruns than Mark. If Mark is to hit more homeruns than Lisa, he must average at least how many more homeruns per week than Lisa?
Answer:
31/4
= 7.75
So Mark has to average more than 7.75 homeruns per week.
Step-by-step explanation:
Mark me as brainliest.
7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 8.17. How much paper of each shade has been used in it?
Answer:
Step-by-step explanation:
diagonal = 32 cm
Area of square = [tex]\dfrac{d^{2}}{2}[/tex]
[tex]=\dfrac{32*32}{2}\\\\=512 \ cm^{2}[/tex]
Diagonal separate the square into two equal triangles.
Area of upper triangle that is shaded black = area of lower triangle = 512/2
= 256 cm²
Isosceles triangle:
a = 6 cm ; b = 6 cm c = 8cm
[tex]s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}[/tex]
Area of black shade paper = 256 + 17.92 = 273.92 cm²
Area of white shade paper = 256 cm²
Area of the isosceles triangle = s(s-a)(s-b)(s-c)
Plot the points in a coordinate plane A(6,-1),B(-1,3),C(2,-3),D(4,-3
3. You have 3 consecutive numbers, with the smallest number n.
a) What are the 7 numbers in the term of n?
b) Hence what is the sum of all the numbers?
( plz write down a step by step explanation ).
-2/9n + 14 = 6
What is this question simplified?
-2/9 n= - 8
2n = 72
N=36
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Answer:
[tex]n = \frac{1}{36} [/tex]
Step-by-step explanation:
[tex] \frac{ - 2}{9n} + 14 = 6[/tex]
[tex] - \frac{ 2}{9n} + 14 = 6[/tex]
[tex] - \frac{2}{9n} = 6 - 14[/tex]
[tex] - \frac{2}{9n} = - 8[/tex]
[tex]2 = 72n[/tex]
[tex]n = \frac{1}{36} [/tex]
Evaluate 6a-b^2/2 + (b/a)^2 if a = 2 and b = 4.
2
6
10.25
36
[tex] \frac{6a - {b}^{2} }{2} + \binom{b}{a} ^{2} [/tex]
a=2 b=4
[tex] \frac{6(2) - {4}^{2} }{2} + \binom{4}{2}^{2} [/tex]
[tex] \frac{12 - 16}{2} + \frac{16}{4} [/tex]
[tex] \frac{ - 4}{2} + 4 [/tex]
[tex] - 2 + 4 = 2[/tex]
answer is option a 2
please mark this answer as brainlist
in a class 1/6 of a children are girls there are five girls in the class how many boys are there in the class
The population of a municipality before 2 years was 60,000 and the rate of annual growth of population is 2%. If the numbers of in-migrants and out-migrants at the end of 2 years were 750 and 410 respectively and 620 people died within this time interval, find the present population of the municipality.
Answer:
62,144
Step-by-step explanation:
60,000 x (1 + 2%)^2 : growth in 2 years
+ 750: in migrants
- 410: out migrants
- 620: died
Answer:
62,144
Step-by-step explanation:
[tex]60,000 \times (1 + 2\%)^{2} [/tex]
➡️ [tex] = 62,424[/tex]
In-migrants:
➡️ [tex]750 - 410 = 340[/tex]
now:
[tex]62,424 + 340 - 620[/tex]
➡️ [tex] = 62,144[/tex]
So, the present of the municipality is 62,144
Tìm x để có 1 mệnh đề đúng và 1 mệnh đề sai : x<1/x
Answer:
x < 0 : 1/2 < 1 ÷ 1/2 ↔ 1/2 < 2 (đúng)
x > 0: 2 < 1/2 (sai)
Step-by-step explanation:
Find the slope of the line going through the points (-10,0)
and (4,0)
Answer:
0
Step-by-step explanation:
To find the slope, we can use the slope formula
m = (y2-y1)/(x2-x1)
= (0-0)/(4- -10)
= (0-0)/(4+10)
= 0/14
=0
Given that x = 2 and y = 3, how much
less is the value of 3x2 – 2y than the
value of 3y2 – 2x?
Answer:
17
Step-by-step explanation:
Evaluate the 2 expressions by substituting x = 2 , y = 3 into them
3x² - 2y
= 3(2)² - 2(3)
= 3(4) - 6
= 12 - 6
= 6
---------------------------
3y² - 2x
= 3(3)² - 2(2)
= 3(9) - 4
= 27 - 4
= 23
Then 23 - 6 = 17
2. A machine fills bags with 24 ounces of M&Ms. After the bags are filled, another
machine weighs them. If a bag's weight differs from the desired 24-ounce weight
by more than 0.25 ounces, the bag is rejected.
Part A: Define a variable and write an absolute value inequality that represents the
weight a bag must be in order to not be rejected.
Can someone help me??
Answer:
Let x = # of ounces in a bag
x ≥ 23.75 and x ≤ 24.25
Step-by-step explanation:
1) The endpoints of FCare (-2,-4 and G(1,0). Find the length of FG-
Answer:
it is [tex]5[/tex]
l.c.m of 84 ,27,35,45
please help
Answer:
3780
Step-by-step explanation:
84 = 2^2 * 3 * 7
27 = 3^3
35 = 5 * 7
45 = 3^2 * 5
lcm = 2^2 * 3^3 * 5 * 7 = 3780
urgent help needed fast
Answer:
Below
Step-by-step explanation:
You can use this formula to find the sum of an arithmetic series
Sn = n / 2 (a1 + an)
You need to find the number of terms in each series before using the formula
Tn = a + (n - 1) d
a) 53 = 5 + (n - 1) 3
n = 17
Sn = 17 / 2 (5 + 53)
= 493
b) 98 = 7 + (n - 1) 7
n = 14
Sn = 14 / 2 (7 + 98)
= 735
c) -102 = 8 + (n - 1) -5
n = 23
Sn = 23 / 2 (8 + (-102))
= - 1081
d) 41/3 = 2/3 + (n - 1) 1
n = 14
Sn = 14 / 2 (2/3 + 41/3)
= 301 / 3 or 100 1/3
Hope this helped! Best of luck <3
hey please help where it says the > thing it says fives, eights, threes
Answer:
[tex]8 \\ = 40 + 24 \\ = 64[/tex]
I hope I helped you^_^
Answer:
[tex]8 \times 8 = 5eights + 3eight \\ 8 \times 8 = 40 + 24 \\ 8 \times 8 = 64 \\ thank \: you[/tex]
Write the value of each expression in standard form. Expression Standard Forr 2hundres×10 in standard form
Please help asap. Look at the picture below
Answer:
2x
Step-by-step explanation:
I'm going to guess that the diagram means that you have 4*(+x) and you subtract 2(x) leaving you with 2x
The ones are a bit harder
(6*1) + (6*-1) = 0
factors of 15,17 ,26 & 80
Answer:
Factors of 15: 1, 3, 5 and 15.
Factors of 17: 1 and 17.
Factors of 26: 1, 2, 13 and 26
Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.
Actually you can find all the answers in the Internet.
The ratio of the radius or diameter or circumference of a circle to its diameter or radius or circumference is approximately 3.14.
Answer:
the question is?
Step-by-step explanation:
Write the following as an algebraic expression;
a) Half the sum of X and y
b) Half the cube of X subtracted from y
Answer:
1/2(x + y)
Step-by-step explanation:
The sum of x and y is x + y
1/2 the sum of x + y is 1/2(x + y)
1/2 x^3
This is subtracted from y
y - 1/2 x^3