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3 years ago

6

the function f(x)=10(2)^x models an insect population after x weeks. to the nearest whole number, what will be the population af

ter 4 wekks

1 answer:

sp2606 [1]3 years ago

6 0

Answer:

Step-by-step explanation:

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If f(x) = 9x10 tan−1x, find f '(x).

djverab [1.8K]

Answer:

$\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle f(x) = 9x^{10} \tan^{-1}(x)$

<u>Step 2: Differentiate</u>

[Function] Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Basic Power Rule: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Arctrig Derivative: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

7 0

3 years ago

Delete this question please. I don't know how to delete this question.

Serhud [2]

I don’t think you can delete questions

8 0

3 years ago

What is the area of the triangle at the right?

Pani-rosa [81]

Answer:

13.16

Step-by-step explanation:

formula= (absin∅)/2

= (4×9×sin47)/2

= 13.16

7 0

3 years ago

The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 48 feet high is s(t) = –16t2 – 32t + 48,

aalyn [17]

Remember that w<span>hen the ball hits the ground, s(t) = 0
</span><span>So we have: -16t^2 - 32t + 48 = 0 </span>
<span>It's time to determine t = (-(-32) +/- sqrt((-32)^2 - 4(-16)(48))) / (2(-16)) </span>
<span>t = (32 +/- sqrt(1024 + 3072)) / (-32) </span>
<span>t = (32 +/- sqrt(4096)) / (-32) </span>
<span>t = (32 +/- 64) / (-32) </span>
<span>t = (48 or -32) / (-32) </span>
<span>t = -1.5 or 1 </span>
<span>Since a negative number doesn't make sense, so t =1</span>
<span>Keep in mind that velocity is the derivative of the height, therefore: </span>
<span>s'(t) = -32t - 32 </span>
<span>s'(t) = -32*1 - 32 </span>
<span>s'(t) = -32 - 32 </span>
<span>s'(t) = -64 </span>
<span>So the answer 64 feet per second dwn</span>

8 0

3 years ago

Which of the following relations is also a function?

RSB [31]

Answer:

all of them

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers