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

1 Answer
Jul 6, 2016

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

Explanation:

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.