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MissTica
3 years ago
13

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
8 0

Answer:

\dfrac{dy}{dx}=- \dfrac{1}{\left(x - 1\right) \left(x + 1\right)}

Step-by-step explanation:

Given:

y = \ln{\left(\dfrac{x + 1}{x - 1}\right)^{\frac{1}{2}}

using the properties of log we can take the power 1/2 and multiply it.

y = \dfrac{1}{2}\ln{\left(\dfrac{x + 1}{x - 1}\right)

now we can differentiate:

\dfrac{dy}{dx} = \dfrac{1}{2}\dfrac{1}{\left(\dfrac{x + 1}{x - 1}\right)}\left(\dfrac{d}{dx}\left(\dfrac{x+1}{x-1}\right)\right)

\dfrac{dy}{dx} = \dfrac{1}{2}\left(\dfrac{x - 1}{x + 1}\right)\left(- \dfrac{2}{\left(x - 1\right)^{2}}\right)

\dfrac{dy}{dx}=- \dfrac{1}{\left(x - 1\right) \left(x + 1\right)}

this is our answer!

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In a school election, Juan received 4 times as many votes as Wayne, Neal recurved twenty less votes than Juan, and Kerry got hal
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Votes received by Wayne is 112

<em><u>Solution:</u></em>

To find: votes received by Wayne

Let the vote received by Wayne be "x"

<em><u>Juan received 4 times as many votes as Wayne</u></em>

Therefore,

Juan votes = 4 times as many votes as Wayne

Juan votes = 4x  ---- eqn 1

<em><u>Neal received twenty less votes than Juan</u></em>

Neal votes = twenty less votes than Juan

Neal votes = Juan votes - 20

Neal votes = 4x - 20 ---- eqn 2

<em><u>Kerry got half as many votes as Neal</u></em>

Kerry votes = half of neal votes

Kerry votes = \frac{4x - 20}{2}  ---- eqn 3

The total votes cast in the election was 1,202

Wayne votes + Juan votes + Neal votes + Kerry votes = 1202

Plug in eqn 1 , eqn 2, eqn 3

x + 4x + 4x - 20 + \frac{(4x - 20)}{2} = 1202\\\\2x + 8x + 8x - 40 + 4x - 20 = 1202 \times 2\\\\22x - 60 = 2404\\\\22x = 2404 + 60\\\\22x = 2464\\\\x = 112

Therefore votes received by Wayne is 112

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