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3 years ago

Find f'(x) for f(x)=cos^2(5x^3).

Mathematics

2 answers:

-BARSIC- [3]3 years ago

6 0

d/dx cos^2(5x^3)

= d/dx [cos(5x^3)]^2

= 2[cos(5x^3)]

= - 2[cos(5x^3)] * sin(5x^3)

= - 2[cos(5x^3)] * sin(5x^3) * 15x^2

= - 30[cos(5x^3)] * sin(5x^3) * x^2

Explanation:

d/dx x^n = nx^(n - 1)

d/dx cos x = - sin x

Chain rule:

d/dx f(g(...w(x))) = f’(g(...w(x))) * g’(...w(x)) * ... * w’(x)

artcher [175]3 years ago

3 0

Step-by-step explanation:

f(x) = cos²(5x³)

f(x) = (cos(5x³))²

Use chain rule to find the derivative:

f'(x) = 2 cos(5x³) × -sin(5x³) × 15x²

f'(x) = -30x² sin(5x³) cos(5x³)

If desired, use double angle formula to simplify:

f'(x) = -15x² sin(10x³)

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Step-by-step explanation:

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A scientist uses 3/4 of an ounce of sulfuric acid each day. How many days does it take him to empty a jar, if each jar contains

Basile [38]

Answer:

32 days

Step-by-step explanation:

Assume that the jar is full initially, containing 24 oz. After how many withdrawals of 3/4 oz will the jar be empty?

24 - (3/4)n = 0, or

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3 years ago

2 Find the slope from the 2 points. (-12,-9) and ( 18, 6) -2 -1/2 2 1/2

lawyer [7]

Step-by-step explanation:

the slope of a line is the ratio y/x.

that means when going from one point to the other, how many units is y changing, when x changes a certain number of units.

so, going from one point to the other here, x changes by 30 units (from -12 to +18). and y changes 15 units (from -9 to 6).

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3 years ago

Which of the relations given by the following sets of ordered pairs is a function?

KonstantinChe [14]

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Answer:

(a) {(5, 2), (-4, 2), (3, 6), (0, 4), (-1, 2)}

Step-by-step explanation:

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3 years ago

Arvin has $10000 to invest. He invests part in a term deposit paying 5%/year, and the remainder in Canada savings bonds paying 3

Delicious77 [7]

Answer:

$4,562.5

Step-by-step explanation:

The amount Arvin has to invest, P = $10,000

The interest paid on the investment in the term deposit = 5%/year

The interest paid om the investment in Canada savings bonds = 3.4%/year

The amount Arvin earned at the of the year as simple interest, A = $413

Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations

x + y = 10,000...(1)

0.05·x + 0.034·y = 413...(2)

Making y the subject of equation (1) and substituting the value in equation (2), we get;

From equation (1), we get, y = 10,000 - x

Plugging the above value of y in equation (2) gives;

0.05·x + 0.034 × (10,000 - x) = 413

∴ 0.05·x - 0.034·x + 340 = 413

x = (413 - 340)/(0.05 - 0.034) = 4,562.5

Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5

(y = 10,000 - x

∴ y = 10,000 - 4,562.5 = 5,437.5

The amount Arvin invested in Canada savings bonds, y = $5,437.5.)

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3 years ago