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Question
Find the second order derivative of the function.
x3 log x
Solution
Let, y = x3 log x
Differentiating both sides with respect to x,
`dy/dx = x^3 d/dx log x + log x d/dx x^3`
`= x^3 * 1/3 + log x * 3x^2`
`= x^2 + 3x^2 log x`
Differentiating both sides again with respect to x,
`(d^2 y)/dx^2 = d/dx x^2 + 3 [x^2 d/dx log x + log x d/dx x^2]`
`= 2x + 3 [x^2 * 1/x + log x * 2x]`
= 2x + 3x + 6x log x
= 5x + 6x log x
= x (5 + 6 log x)
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