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madreJ [45]
3 years ago
12

Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

Mathematics
1 answer:
almond37 [142]3 years ago
6 0

Answer:

\frac{1}{1+e^x}

Step-by-step explanation:

We are given: y = \ln( \frac{e^x}{1+e^x} )

The Division and Logarithm properties of the Derivative will be used.

y' =\frac{\frac{e^x(1+e^x)-e^xe^x}{(1+e^x)^2}}{\frac {e^x}{1+e^x}} =\frac{1}{1+e^x}

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nevsk [136]

Answer: Option C)1 over 15 minus 1 over x equals 1 over 20

Explanation:

Since, Micah can fill a box with books in 15 minutes.

Therefore, the work done by Micah in one minute= 1/15

Also, Sydney takes the books out puts them on a shelf.

And the times taken by Micah when Sydney is also taking the books outside from the self= 20 minutes

Therefore, the work done by Micah in one minute when Sydney  taking books out of the box= 1/20

Let Sydney alone takes x minutes to take books outsides the shelf.

Then, work done by Sydney in one minute=1/x

Thus, the work done by Sydney( by taking books out of the box)=  the work done by Micah - work done by Micah and Sydney simultaneously= 1/15-1/20

⇒1/x=1/15-1/20

⇒1/15-1/20=1/x

⇒1/15-1/x=1/20 is the required expression.

Therefore, Option C is correct.



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