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]
MissSpanishI wrote a cheque for $10 and he threw my 2 dollar how much do I have left
Answer:
you have $ 8
Step-by-step explanation:
cheque wrote ,=$10
and he threw =$2
then total $ left will be $8
please mark me brainleast
Solve for W.
4w=5.12
Answer:
x =1.28
Step-by-step explanation:
4w=5.12
Divide each side by 4
4w/4 = 5.12/4
x =1.28
3. For the sequence defined by tn= 3n + 8,
find each indicated term.
a) t1
b) t7
c) t14
Step-by-step explanation:
Hi there!
According to the question;
nth term (tn) = 3n+8
a).
T1 = 3*1+8
= 11
b).
t7 = 3*7+8
= 29
c).
t14 = 3*14+8
= 50
Therefore, t1 = 11, t7 = 29, t14 = 50.
Hope it helps!
Answer:
11, 29, 50
Step-by-step explanation:
To find the appropriate term , substitute the term number into the rule, that is
(a) t₁ = 3(1) + 8 = 3 + 8 = 11
(b) t₇ = 3(7) + 8 = 21 + 8 = 29
(c) t₁₄ = 3(14) + 8 = 42 + 8 = 50
Can someone tell me the asnwer to this ASAP?
Answer:
[tex]2\sqrt{2} \\2[/tex]
Step-by-step explanation:
[tex]\sqrt{8} = \sqrt{4*2} = \sqrt{4} * \sqrt{2} = 2*\sqrt{2} = 2\sqrt{2} \\\\\sqrt[3]{8} = \sqrt{2*2*2} = 2[/tex]
Answer:
I noticed that [tex]\sqrt{8\\}[/tex] does not have 3 on it like the second one. And i wonder that the answers would be different from each other
[tex]2\sqrt{2}[/tex]
2
A number line shows 1 1/5, −2 2/5, and −1 3/5. Which statement is NOT true?
Answer:
The answer Is A 1 1/5 < -2 2/5
Step-by-step explanation:
It says that this statement is true because 1 1/5 is to the left of -2 2/5 on the number line but it is actually to the right because -2 2/5 is negative while 1 1/5 is positive therefore making it larger and the correct statement would be that 1 1/5 > -2 2/5
someone help me asap
Answer:
19/20 cups
Step-by-step explanation:
Add the amounts together
1/4 + 7/10
Get a common denominator of 20
1/4 *5/5 + 7/10 *2/2
5/20 + 14/20
19/20
Answer:
19/20
Step-by-step explanation:
find a common denominator then do the same with the numerator then add.
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
1.Write the linear equation that models the equation?
2.What is the cost per T-shirt?
3.What is the standard shipping and handling bag?
Step-by-step explanation:
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
Then we have to writer a linear equation, for which I got: y-27/4x+25. We also had to find the cost per t-shirt, for which I got: $31.75. The last part I don't understand, however: fidn the shipping and handling charge.
The second word problem is:
It costs Consolidated Cereals Corporation $1050 to produce 100 boxes of corn flakes and $1250 to produce 500 boxes. I found the cost function: c(x)=1/2x+1000 but don't know how to determine the fixed cost and the variable cost per box (mainly because I have no idea what those are.)
Cost= m x+b
x is the cost per shirt, b is the handling charge
295=40m+b
565=80m+b
subtract the first equation from the second:
370=40x solve for m, the cost of each shirt. Then solve for b, put all that into y= mx+b
One the second question,
Cost= variable cost * n + Fixedcosts or
cost= n*v+F
1250=500v+f
1050=100v+f
subtract the second equation from the first
200=400v solve for v, and it is 1/2 dollar. Solve for f, the fixed cost, and it looks as if it is 1000 dollars.
Im bad at money :/ do please help me
The third answer
1 quarter, 6 dimes, 1 nickel, 7 pennies
