What is the second derivative of #f(x)= ln sqrt(e^x)#?

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Answer 1 · 2016-01-15T14:58:27

#0#

Let #t = sqrt(e^x) = e^(x/2)#

#(dt)/(dx) =1/2*e^(x/2)#

#f(t) = ln t#

#(df)/(dt) = 1/t#

#(df)/(dx) = (df)/(dt)*(dt)/(dx)#

#= 1/t *(e^(x/2))/2 =(e^(x/2))/(2e^(x/2)) = 1/2#

#f''(x) = d/dx(1/2) = 0#