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Julli [10]
3 years ago
12

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Mathematics
1 answer:
adoni [48]3 years ago
3 0

Answer: The required derivative is \dfrac{8x^2+18x+9}{x(2x+3)^2}

Step-by-step explanation:

Since we have given that

y=\ln[x(2x+3)^2]

Differentiating log function w.r.t. x, we get that

\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [x'(2x+3)^2+(2x+3)^2'x]\\\\\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [(2x+3)^2+2x(2x+3)]\\\\\dfrac{dy}{dx}=\dfrac{4x^2+9+12x+4x^2+6x}{x(2x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{8x^2+18x+9}{x(2x+3)^2}

Hence, the required derivative is \dfrac{8x^2+18x+9}{x(2x+3)^2}

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Marisa decided to raise the price of her earrings so that she will make a profit of $5.00 on each pair. She has
Varvara68 [4.7K]

Marisa, who raise the price of her earrings so that she will make a profit of $5.00 on each pair, expect to make a profit with her company.

<h3>What is the unit price?</h3>

The unit price is the amount of money required to buy one unit of a item or goods.

To find the unit price, divide the total cost of the goods to the total number of goods.

The cost of repair will now be $60. Thus, the total cost of 50 earrings is,

C=60\times50\\C=3000

Marisa decided to raise the price of her earrings so that she will make a profit of $5.00 on each pair. Thus, the new selling price of her earring is,

P=60+5\\P=65

The sale's price of 50 earrings is,

P=50\times65\\P=3250

She has also improved the quality control so that only 1 pair in 50 need to be returned for repair. Thus, the cost price of one earring has to be removed from the sales price of 50 earrings as,

P=3250-60\\P=3190

The profit made by her company on 50 earrings is

p=P-C\\p=3190-3000\\p=190

Thus, Marisa, who raise the price of her earrings so that she will make a profit of $5.00 on each pair, expect to make a profit with her company.

Learn more about the unit price here;

brainly.com/question/25879801

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2 years ago
What is the converse of the conditional statement?
dem82 [27]

Answer:

according to me 1st option seems to be correct❤️

5 0
3 years ago
Northern Bank has two types of account. Both accounts pay compound interest. Cash savings account Interest 2.5% per annum Shares
musickatia [10]

Answer: Ben will have the most interest.

Step-by-step explanation:

Ali after 3 years.

To use compound interest, the formula is:

= Investment * ( 1 + rate) ^ no. of periods

= 2,000 * ( 1 + 2.5%)³

= £‭2,153.78

Interest = Amount after 3 years - investment

= 2,153.78 - 2,000

= £153.78

Ben after 3 years.

= 1,600 * (1 + 3.5%)³

= £1,773.95

Interest = 1,773.93 - 1,600

= £173.93

4 0
3 years ago
700 is 35% of what number??
harina [27]

Answer:

245

Step-by-step explanation:

35                    x

-------             --------

100               700

then you cross multipy and you get

24500

------------------

100

cross out the zeros

and get 245

8 0
3 years ago
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