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Tasya [4]
3 years ago
11

What is the derivative of the following function? f(x) = 4x^6/cos^5(x)

Mathematics
1 answer:
KIM [24]3 years ago
5 0

Answer:

f'(x) = \frac{24x^{5} \cos x + 20x^{6}\sin x}{\cos^{6}x }

Step-by-step explanation:

We have to find the derivative of the following function:

f(x) = \frac{4x^{6} }{\cos^{5} x }

Now, differentiating both sides with respect to x we get,

f'(x) = \frac{\cos^{5}x (24x^{5}) - 4x^{6}(5\cos^{4}x )(- \sin x)}{(\cos^{5}x )^{2}}

⇒ f'(x) = \frac{ 24x^{5} \cos x + 20 x^{6}\sin x}{\cos^{6}x } (Answer)

{Since, we know that, \frac{d(mx^{n} )}{dx} = m \times n x^{(n - 1)} and \frac{d(\cos^{n} x)}{dx} = n \cos^{(n - 1)} x(- \sin x) }

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Answer:

3)

Step-by-step explanation:

An equation is linear if equal changes in x produce equal changes in y.

Let's look at each choice.

1)

A decrease of 10% per year. That means each year, the value of the car is 0.9 times the value of the previous year.

For example, if the original value was $10,000, after 1 year, it is worth 0.9 * $10,000 = $9,000. In 1 year it lost $1,000. In the next year, its value is now 0.9 * $9,000. The value at the end of the 2nd year is $8,100. In the second year, it lost $900 in value. In one period of 1 year it lost $1000 in value. In another equal period of 1 year, it lost $900 in value. A change of 1 year in time produces different changes in loss of value, so it is not linear.

2)

Here, the number doubles every year. Let's say it starts with 100 fish. After 5 years, it has 200 fish. In a change of 5 years in x, the change in y is 100. In the next 5 years, it goes from 200 fish to 400 fish. The change in the second period of 5 years is 200. We see that a change of 5 years can produce a change of 100 fish, but another change of 5 years can produce a change is 100 fish. Since for equal changes in x, the changes in y are not all equal, this is not linear.

3)

Here for every change of 1 day in x, the change in y is 2 liters. Each change of 1 in x always produces a change of 2 in y. This is linear.

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Each 2 hours, the amount of caffeine is 2/3 of what it was before. This is similar to the choice 1), and it is not linear.

Answer: 3)

7 0
3 years ago
Simplify the expression below:<br> (-5x² + 2) - (4x² – 5x - 9)
lozanna [386]

Answer:

-9x² + 5x + 11

Step-by-step explanation:

-5x² + (-4x²) + 5x + 2 + 9

-9x² + 5x + 11

3 0
2 years ago
247: 10^2 and 247*10^2 what is the different about the two answers
CaHeK987 [17]
Um the 2nd one has a star
5 0
3 years ago
This item is $9000 dollar and it is 90% off how much is the item? Step by step?
Daniel [21]

Answer:

The item costs $900 after the 90% off.

Step-by-step explanation:

After the 90% off discount, the item costs (100% - 90%) the cost of the original price.

Hence, \$9000 \cdot (100\% - 90\%)

= \$9000 \cdot 10\%

= \$900

Hope this helped!

5 0
3 years ago
Read 2 more answers
Please help with the following question
Alex17521 [72]
P1=(0,0)=(x1,y1)→x1=0, y1=0
P2=(3,-2)=(x2,y2)→x2=3, y2=-2

Slope: m=(y2-y1)/(x2-x1)
m=(-2-0)/(3-0)
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Point-slope equation:
y-y1=m(x-x1)
y-0=(-2/3)(x-0)
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Answer: The equation of the line is: y=-(2/3)x
5 0
3 years ago
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