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Dafna11 [192]
2 years ago
15

Use the inverse function-inverse cofunction

Mathematics
1 answer:
vivado [14]2 years ago
4 0

Answer:

arccot(x)'=-\frac{1}{1+x^2}

Step-by-step explanation:

<u>Use implicit differentiation:</u>

y=arccot(x)

cot(y)=x

\frac{1}{tan(y)}=x

\frac{cos(y)}{sin(y)}=x

\frac{dy}{dx}(\frac{cos(y)}{sin(y)})=\frac{dy}{dx}(x)

\frac{sin(y)(-sin(y))-cos(y)cos(y)}{sin^2(y)}*\frac{dy}{dx}=1 (Quotient Rule: \frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2} )

\frac{-sin^2(y)-cos^2(y)}{sin^2(y)}*\frac{dy}{dx}=1

\frac{-(sin^2(y)+cos^2(y))}{sin^2(y)}*\frac{dy}{dx}=1

\frac{-1}{sin^2(y)}*\frac{dy}{dx}=1

-csc^2(y)\frac{dy}{dx}=1

\frac{dy}{dx}=\frac{1}{-csc^2(y)}

\frac{dy}{dx}=-sin^2(y)

\frac{dy}{dx}=-sin^2(arccot(x))

See the attached picture to understand how to evaluate the mixed composition of trig functions using a right triangle.

Therefore, the derivative of arccot(x) is -\frac{1}{\sqrt{1+x^2}}.

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Step-by-step explanation:

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3 years ago
Round the distance traveled in kilometers to the nearest ten thousand
damaskus [11]

Let’s assume the following given:

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Find:

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Solution:


In order to get the distance, we multiply speed and time.


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Distance = 129 m/s * 2,900,000 s

Distance = 374,100,000 m

Next, we will convert the distance from meters to kilometers by dividing the distance with 1,000 m.

374,100,000 m / 1,000 m = 374,100 km

<span>The last step would be converting the travelled distance in kilometers to the nearest ten thousand.

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masya89 [10]

Answer:

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Step-by-step explanation:

7 0
2 years ago
Question is in attached picture below
valina [46]

Answer:

My answer may not be accurate, but try (-4, 2)

I recommend using Khan Academy if you still don't understand the concept. (no shame btw)

Step-by-step explanation:

Here is a thorough explanation.

Interval notation is a way of writing subsets of the real number line . A closed interval is one that includes its endpoints: for example, the set {x | −3≤x≤1} . To write this interval in interval notation, we use closed brackets [ ]: [−3,1]

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Witch is longer 2 feet or 30 inches
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Since 1 foot is equal to 12 inches,        12 inches x 2 feet = 24 inches
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30 inches is longer
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3 years ago
Read 2 more answers
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