How do you find the second derivative of #ln(x/2)# ?

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Answer 1 · 2016-07-06T07:04:41

#:. (d^2y)/dx^2=-1/x^2#

Let #y=ln(x/2)#

We have to find #(d^2y)/dx^2.#

We start with #y=ln(x/2)# and use Rules of Logarithmic Fun. to see that,

#y=lnx-ln2#

#:. (dy)/dx=1/x=x^-1.#

#:. (d^2y)/dx^2=d/dx{dy/dx}....[Defn.] = d/dx(x^-1)=-1*x^(-1-1).#

#:. (d^2y)/dx^2=-1/x^2.#