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Find the second order derivatives of the functions given in \(\log x \)

$\begin{array}{1 1} \large\frac{-1}{x^3} \\\large\frac{1}{x^2} \\\large\frac{-1}{x} \\\large\frac{-1}{x^2} \end{array} $

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1 Answer

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Toolbox:
  • $y=f(x)$
  • $\large\frac{dy}{dx}$$=f'(x)$
  • $\large\frac{d^2y}{dx^2}=\frac{d}{dx}\big(\frac{dy}{dx}\big)$
  • $\large\frac{d}{dx}$$\log x=\large\frac{1}{x}$
Step 1:
Differentiating with respect to $x$
$\large\frac{dy}{dx}=\frac{1}{x}$
$\quad\;=x^{-1}$
Step 2:
$\large\frac{d^2y}{dx^2}=\frac{d}{dx}$$(x^{-1})$
$\quad\;\;=-1.x^{-2}=\large\frac{-1}{x^2}$
answered May 10, 2013 by sreemathi.v
 
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