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Find the second order derivatives of the functions given in \( x^{\large 20} \)

$\begin{array}{1 1} 18x^{\large 19} \\ 20x^{\large 20} \\ 380x^{\large 18} \\20x^{\large 19} \end{array} $

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Toolbox:
  • $\large\frac{d}{dx}$$(x^{\large n})=nx^{\large n-1}$
  • $y=f(x)$
  • $\large\frac{dy}{dx}$$=f'(x)$
  • $\large\frac{d^2y}{dx^2}=\frac{d}{dx}\big(\frac{dy}{dx}\big)$
Step 1:
$y=x^{\large 20}$
Differentiating with respect to $x$
$\large\frac{dy}{dx}$$=20x^{\large 19}$
Step 2:
$\large\frac{d^2y}{dx^2}=\frac{d}{dx}\big(\frac{dy}{dx}\big)$
$\large\frac{d^2y}{dx^2}=\frac{d}{dx}$$(20x^{\large 19})$
$\qquad=20\large\frac{d}{dx}$$(x^{\large 19})$
$\qquad=20.19.x^{\large 18}$
$\qquad=380x^{\large 18}$
answered May 10, 2013 by sreemathi.v
 
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