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2 years ago

Use the chain rule to find the derivative of each of the following :

Mathematics

1 answer:

ankoles [38]2 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

Using the chain rule

Given

y = f(g(x)), then

$\frac{dy}{dx}$ = f'(g(x)) × g'(x)

(a)

y = $\frac{2}{(3x^2-x+7)^3}$ = 2 ( $3x^2-x+7)^{-3}$

$\frac{dy}{dx}$ = 2. - 3 $(3x^2-x+7)^{-4}$ × $\frac{d}{dx}$ (3x² - x + 7)

= - 6 $(3x^2-x+7)^{-4}$ × (6x - 1)

= $\frac{-6(6x-1)}{(3x^2-x+7)^4}$

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

(b)

y = $(4x-10)^{10}$

$\frac{dy}{dx}$ = 10 $(4x-10)^{9}$ × $\frac{d}{dx}$ (4x - 10)

= 10 $(4x-10)^{9}$ × 4

= 40 $(4x-10)^{9}$

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In 2000, the circulation of a local newspaper was 3,250. In 2001, its circulation was 3,640. In 2002, the circulation was 4,100.

vodka [1.7K]

Percent increase from 2000 to 2001 is 12% and from 2001 to 2002 is 12.6%. Thus period of 2001 to 2002 has higher increase percentage.

Solution:

Given that,

Total circulation of local newspaper in 2000 = 3250

Total circulation of local newspaper in 2001 = 3640

Total circulation of local newspaper in 2002 = 4100

Finding percent of increase in the newspaper’s circulation from 2000 to 2001:

$\text { Percent increase from } 2000 \text { to } 2001=\frac{\text { change in circulation from 2001 - 2000 }}{\text { circulation in } 2000} \times 100$

$\begin{array}{l}{=\frac{3640-3250}{3250} \times 100} \\\\ {=\frac{390}{3250} \times 100=12 \%}\end{array}$

Finding percent of increase in the newspaper’s circulation from 2001 to 2002:

$\begin{array}{l}{\text { Percent increase from } 2001 \text { to } 2002=\frac{\text { change in circulation }}{\text {circulation in } 2001} \times 100} \\\\ {=\frac{4100-3640}{3640} \times 100} \\\\ {=\frac{460}{3640} \times 100=12.6 \%}\end{array}$

As we can see 12% < 12.6%

So period of 2001 to 2002 has higher increase percentage.

7 0

3 years ago

What is 383,342 rounded?

solmaris [256]

It could be 400,000 or 383,000

6 0

3 years ago

Use the information in the diagram to find the length of segment AD. Round your answer to the nearest hundredth.

Lana71 [14]

Based on the lengths of the given triangles and the length of segment BD, the length of segment AD is 22.20.

<h3>What is the length of segment AD?</h3>

The triangle ABC is a right angled triangle with segment AB being the hypothenuse.

We can therefore find this length using the Pythagoras Rule:

Hypothenuse ² = a² + b²

Hypothenuse ² = 28.6² + 23.2²

Hypothenuse ² = 1,356.20

Hypothenuse = √1,356.20

= 36.83

Length of AD:
= AB - BD

= 36.83 - 14.60

= 22.2

Find out more on the Pythagorean theorem at brainly.com/question/343682.

#SPJ1

7 0

2 years ago

CAN SOMEONE HELP ME UNDERSTAND THIS PLEASE

ICE Princess25 [194]

YEAH OFC SHAWTY!

so for A its -4^11 because if the powers have the same base and they are being multiplied you add the powers

For B its the same idea, they have the same base, and are being multiplied so you add the powers- 13^9

For C its similar, you have the same base, but since its Dividing, you subtract the powers. So, 9^5
for D you pretend like the denominator has a power of 1 and subtract. So its -24^5-24^1 which hopefully puts it into perspective of being -24^4 becuase we subtracted the powers

I cant do 2 right now, but i will in a minute

And for 3 his mistake is that they arent the same bases so he cant add the powers, he should have converted them to the same base first.

7 0

3 years ago

What is the value of v? 4/5(v−7)=2

Nostrana [21]

4/5(v - 7) = 2...distribute the 4/5 thru the parenthesis
4/5v - 28/5 = 2 ...multiply everything by 5
4v - 28 = 10...add 28 to both sides
4v = 10 + 28
4v = 38
v = 38/4 reduces to 19/2 or 9 1/2 <==

3 0

3 years ago

Read 2 more answers