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January 29, 2015

January 29, 2015

Posted by **Jes** on Tuesday, October 30, 2012 at 12:42am.

1. f(x)=2(e^x) - x^2

2. f(x)=e^x/(e^x +1)

3. y=10^(√x)

- Math/Derivative -
**Steve**, Tuesday, October 30, 2012 at 11:03am#1. (e^x)' = e^x, so

f' = 2e^x - 2x

#2.

quotient rule:

f' = (e^x(e^x+1) - e^x*e^x)/(e^x+1)^2

= (e^2x + e^x - e^2x)/(e^x+1)^2

= e^x/(e^x+1)^2

or, knowing that e^x/(e^x+1) = 1 - 1/(e^x+1)

f' = e^x/(e^x+1)^2

#3. Recall that (a^u)' = ln a a^u u'

y' = ln 10 10^√x * 1/(2√x) = ln10/(2√x) 10^(√x)

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