Find the second order derivatives of the function given in Exerci… - Vidyadip

Question

Find the second order derivatives of the function given in Exercise:
$\text{x}^3\log\text{x}$

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Answer

Let $\text{y}=\text{x}^3\log\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\text{x}^3.\frac{1}{\text{x}}+\log\text{x}.3\text{x}^2=\text{x}^2+3\text{x}^2\log\text{x}=\text{x}^2(1+3\log\text{x})$
$\therefore\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{x}^2.\frac{3}{\text{x}}+(1+3\log\text{x}).2\text{x}$
$=3\text{x}+2\text{x}(1+3\log\text{x})=\text{x}[3+2(1+3\log\text{x})]$
$=\text{x}[3+2+6\log\text{x}]=\text{x}(5+6\log\text{xz})$

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