Find the second order derivatives of the following functions: y= … - Vidyadip

Question

Find the second order derivatives of the following functions:
$\text{y}=\log(\log\text{x})$

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Answer

We have,
$\text{y}=\log(\log\text{x})$
Differentiating w.r.t.x, we get
$\frac{\text{dy}}{\text{dx}}=\frac{1}{\log\text{x}}\times\frac{1}{\text{x}}=\frac{1}{\text{x}\log\text{x}}$
Differentiating w.r.t.x, we get
$ \frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{0-(\log\text{x}+1)}{(\text{x}\log\text{x})^2}=-\frac{(1+\log\text{x})}{(\text{x}\log\text{x})^2}$

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