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Question
Find the second order derivatives of the following function x3 log x ?
Solution
We have,
\[y = x^3 \log x\]
\[\text { Differentiating w . r . t . x, we get }\]
\[\frac{d y}{d x} = 3 x^2 \log x + x^3 \times \frac{1}{x}\]
\[ = 3 x^2 \log x + x^2 \]
\[\text { Differentiating again w . r . t . x, we get }\]
\[\frac{d^2 y}{d x^2} = 6x \log x + 3 x^2 \times \frac{1}{x} + 2x\]
\[ = 6x \log x + 5x\]
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