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Can someone help me figure out the answer and..possibly show the steps.. to finding the derivative of these 3 questions..

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

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

3. y=10^(√x)

  • Math/Derivative -

    #1. (e^x)' = e^x, so
    f' = 2e^x - 2x

    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)

  • Math/Derivative -


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