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Hunter-Best [27]
3 years ago
12

Differentiate the function. f(x) = sin(9 ln(x))

Mathematics
1 answer:
gayaneshka [121]3 years ago
5 0

Answer: f'(x)=\dfrac{9\cos(9\ln (x))}{x}.

Step-by-step explanation:

The given function is

f(x)=\sin(9\ln (x))

Using chain rule differentiate w.r.t. x.

f'(x)=\cos(9\ln (x))\dfrac{d}{dx}(9\ln (x))      \left[\because \dfrac{d}{dx}\sin x=\cos x\right]

f'(x)=\cos(9\ln (x))\left[9\dfrac{d}{dx}(\ln (x))\right]

f'(x)=\cos(9\ln (x))\left[9\times \dfrac{1}{x}\right]       \left[\because \dfrac{d}{dx}\ln x=\dfrac{1}{x}\right]

f'(x)=\dfrac{9\cos(9\ln (x))}{x}

Therefore, f'(x)=\dfrac{9\cos(9\ln (x))}{x}.

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It would be 15 inches long.

Simply subtract the other part from the total.

24-9=15
8 0
4 years ago
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- The center of a circle is located at (1, 4) and a point on the circle is located at (5,
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Answer:

(x - 1)^2 + (y - 4)^2 = 4^2

Step-by-step explanation:

Here you're given the center:  (1, 4)  :  (h, k), and so the equation becomes

(x - 1)^2 + (y - 4)^2 = r^2

To find r^2 and r, substitute 5 for x and 4 for y, obtaining:

(5 - 1)^2 + (4 - 4)^2 = r^2

Then:  4^2 = r^2, and so r must be 4.  The final version of the equation is

(x - 1)^2 + (y - 4)^2 = 4^2

6 0
3 years ago
Too much to type!! So here is a photo instead
klasskru [66]

Answer:

<em><u>9 months</u></em>

Step-by-step explanation:

1. write out equation

100 + 22x = 298

2. Subtract 100 from both sides

22x = 198

3. Divide 22 from each side

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Help!
GaryK [48]

Answer:

The computation of the angles show that the value of sin x and cos y will be 4/5 and 3/5 respectively.

How to calculate the angles?

From the information, we've to compute the length of the hypothenuse using Pythagoras theorem.

Therefore, 4² + 3² = hypothenuse²

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Therefore, sin x = opposite/hypothenuse = 4/5

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In conclusion, the values are 4/5 and 3/5.

Step-by-step explanation:

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