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zhenek [66]
1 year ago
13

Differentiate each function with respect to x. Show steps

Mathematics
1 answer:
konstantin123 [22]1 year ago
4 0

The derivative of the function is f'(x) = 9x² tan x⁴ + 4x³(3x³ + 2) sec² x⁴.

<h3>What is the derivative of a function?</h3>

When a single-variable function exists at a given input value, its derivative is represented by the slope of the tangent line to the function's graph at that point.

The given function is f(x) =tan x⁴ · (3x³ + 2).

Differentiate the function with respect to x:

f'(x) = tan x⁴ · 9x² + (3x³ + 2) sec² x⁴· 4x³

      = 9x² tan x⁴ + 4x³(3x³ + 2) sec² x⁴

Hence, the derivative of the function is

f'(x) = 9x² tan x⁴ + 4x³(3x³ + 2) sec² x⁴

Learn more about the derivatives:

brainly.com/question/25324584

#SPJ1

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A house and a lot are appraised at $191,700. If the value of the house is five times the value of the lot, how much is the house
gladu [14]

Answer:

$159,750

Step-by-step explanation:

191700=5x+x     x=lot

191700/6=31950

x=31950

house=5x

5(31950)

house= 159750

4 0
4 years ago
Use the confidence level and sample data to find a confidence interval
stepan [7]

Answer:

The confidence interval at at 99% level of confidence is <em>93.7 ≤ μ ≤ 96.9</em>.<em> </em>

Step-by-step explanation:

Step 1:

We must first determine the z-value at a confidence level of 99%.

Therefore,

99% = 100%(1 - 0.01)

Thus,

α = 0.01

Therefore, the z-value will be

z_(α/2) = z_(0.01/2) = z_0.005 = 2.58

(The z-value is read-off from the z table from the standard normal probabilities.)

Step 2:

We can now write the confidence interval:

X - z_(α/2) [s/√(n)] ≤ μ ≤ X + z_(α/2) [s/√(n)]

95.3 - 2.58(6.5/√(104))  ≤ μ ≤  95.3 + 2.58(6.5/√(104))

       <em>93.7 ≤ μ ≤ 96.9</em>

Therefore, confidence interval is <em>93.7 ≤ μ ≤ 96.9 </em>which means that we are 99% confident that the true mean population lies is at least 93.7  and at  most 96.9.

4 0
4 years ago
A store receives 2,000 decks of popular trading cards. The number of decks of cards is a function, d, of the
BARSIC [14]

Answer:

-143.4 for 0-5 and -38 for 15-20

Step-by-step explanation:

3 0
3 years ago
1. Solve 4x = 45 - 11x.
Andrej [43]
The work is shown below, x=3. i hope this helps!

8 0
3 years ago
How do you divide $306 into the ratio of 9:5:3? Can someone give me some advice on how to solve this problem?
GarryVolchara [31]
In order to divide $306 into the ratio of 9 to 5 to 3, first you have to make each section of the ratio represented by a variable, and put it into an equation.

9x + 5x + 3x = 306

Our next step is to simplify the left side of the equation by combining all of the like terms, the ones that contain variables.

17x = 306

Finally, to solve this equation, you have to divide both sides by 17 to isolate the variable x on the left side of the equation.

x = 18

However, this is not our answer as it isn't in a ratio format and doesn't really make sense. To find our ratio, we have to multiply each of our initial numbers (9, 5, and 3) by our variable, x.

9 * 18 = 162
5 * 18 = 90
3 * 18 = 54

You can verify that these numbers are correct because if you add them together you get 306.

Your final ratio is 162:90:54.

Hope this helps! :)

If you have a separate specific question about pre-tax prices and PMed me the link, I'd be happy to help you.
4 0
3 years ago
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