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kifflom [539]
3 years ago
8

Find f'(x) and state the domain of f': f(x) = In (2x^2+1)

Mathematics
1 answer:
-Dominant- [34]3 years ago
5 0

Answer:

f'(x) = \frac{4x}{2x^2+1}

Domain: All Real Numbers

General Formulas and Concepts:

<u>Algebra I</u>

  • Domain is the set of x-values that can be inputted into function f(x)

<u>Calculus</u>

The derivative of a constant is equal to 0

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Chain Rule: \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Derivative: \frac{d}{dx} [ln(u)] = \frac{u'}{u}

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = ln(2x² + 1)

<u>Step 2: Differentiate</u>

  1. Derivative ln(u) [Chain Rule/Basic Power]:                          f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}
  2. Simplify:                                                                                       f'(x) = \frac{1}{2x^2+1} \cdot 4x
  3. Multiply:                                                                                                     f'(x) = \frac{4x}{2x^2+1}

<u>Step 3: Domain</u>

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.

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-4r-8(r-6)=7(5r-1)+8
KATRIN_1 [288]

Answer:

r = 1

Step-by-step explanation:

In this question, we have to solve for the vallue of "r". We will use the distributive property shown below to ease our process.

Distributive Property:

a(b+c) = ab + ac

Now, lets solve this:

-4r-8(r-6)=7(5r-1)+8\\-4r-8r+48=35r-7+8\\-12r+48=35r+1\\48-1=35r+12r\\47=47r\\r=\frac{47}{47}\\r=1

As we have seen the value of r is "1"

6 0
3 years ago
Help<br><br><br><br><br><br><br><br><br><br> Sjsjjjsjajajahjajaja
motikmotik

Answer:

hi

Step-by-step explanation:

{5}^{2}  +  {x}^{2}  =  {7}^{2}  \\ 25 +  {x}^{2}  = 49 \\  {x}^{2}  = 49 - 25 \\  {x}^{2}  = 24 \\ x =  \sqrt{24}

have a nice day

6 0
2 years ago
Find a ·<br> b. |a| = 80, |b| = 50, the angle between a and b is 3π/4.
mart [117]

Answer:

a\cdot b=-2000\sqrt{2}

Step-by-step explanation:

Given information: |a| = 80, |b| = 50, the angle between a and b is 3π/4.

We need to find the dot product  a · b.

The formula of dot product is

a\cdot b=|a||b|\cos \theta

where, θ is the angle between a and b.

Substitute the given values in the above formula.

a\cdot b=(80)(50)\cos (\frac{3\pi}{4})

a\cdot b=4000\cos (\pi-\frac{\pi}{4})

a\cdot b=-4000\cos (\frac{\pi}{4})           [\because \cos (\pi-\theta)=-\cos \theta]

a\cdot b=-4000\frac{1}{\sqrt{2}}

a\cdot b=-\frac{4000}{\sqrt{2}}

Rationalize the above equation.

a\cdot b=-\frac{4000}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}

a\cdot b=-\frac{4000\sqrt{2}}{2}

a\cdot b=-2000\sqrt{2}

Therefore, the value of a · b is a\cdot b=-2000\sqrt{2}.

7 0
3 years ago
Read 2 more answers
The coach recorded the time it took 15 students to run a mile. The times are as follows: 9:23, 8:15, 9:23, 9:01, 6:45, 6:55, 7:2
r-ruslan [8.4K]

Answer:

Therefore, the four intervals are

(1)    6 - 6.59

(2)   7 - 7.59      

(3)    8 - 8.59      

(4)    9 - 9.59

The four frequencies are

(1)   4

(2)   3

(3)   1    

(4)  6

Step-by-step explanation:

From the data, we have

                     Interval                                                       Frequency

1st                 6 - 6.59                                                        4

2nd               7 - 7.59                                                        3

3rd                8 - 8.59                                                        1

4th                 9 - 9.59                                                       6

Therefore, the four intervals are

(1)    6 - 6.59

(2)   7 - 7.59      

(3)    8 - 8.59      

(4)    9 - 9.59

The four frequencies are

(1)   4

(2)   3

(3)   1    

(4)  6

5 0
3 years ago
-8
nevsk [136]

Answer:

  take your pick. Each has its own reason.

Step-by-step explanation:

As with a lot of "doesn't belong" problems, the one that is different depends on your criteria. In the attached figure, each one "doesn't belong" for a different reason. Those reasons are listed below each number line.

__

I might choose the lower left: "addition, not subtraction", as it is the only one with arrows in the same direction. That makes its difference from the others more obvious, perhaps.

6 0
3 years ago
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