Q9  Find the second order derivatives of the functions given in Exercises 1 to 10. 

       \log (\log x )

Answers (1)

Given function is
y = \log(\log x)
Now, differentiation w.r.t. x
\frac{dy}{dx}=\frac{d(\log(\log x))}{dx}=\frac{1}{\log x}.\frac{1}{x}= \frac{1}{x\log x}
Now, second order derivative is
\frac{d^2y}{dx^2}= \frac{-1}{(x\log x)^2}.(1.\log x+x.\frac{1}{x}) = \frac{-(\log x+1)}{(x\log x)^2}
Therefore,  second order derivative is \frac{d^2y}{dx^2} = \frac{-(\log x+1)}{(x\log x)^2}

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