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

Question

Find the second order derivatives of the following functions:
$\text{y}=\text{x}^3\log\text{x}$

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Answer

We have
$\text{y}=\text{x}^3\log\text{x}$
differentiating w.r.t.x, we get
$\frac{\text{dy}}{\text{dy}}=3\text{x}^2\log\text{x}+\text{x}^3\times\frac{1}{\text{x}}$
$=3\text{x}^2\log\text{x}+\text{x}^2$
differentiating w.r.t.x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=6\text{x}\log\text{x}+3\text{x}^2\times\frac{1}{\text{x}}+2\text{x}$
$=6\text{x}\log\text{x}+5\text{x}$

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