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Question
If y = x log x, then `(d^2y)/dx^2`= _____.
Solution
If y = x log x, then `(d^2y)/dx^2`= `bb(underline(1/x))`
Explanation:
y = x log x
Differentiating both sides,
`dy/dx = x * d/dx(logx) + logx * d/dx(x)`
= `x * 1/x + logx` = 1 + logx
Again differentiating w.r.t.x,
`d/dx(dy/dx) = d/dx(1) + d/dx(logx)`
`(d^2y)/(dx^2) = 0 + 1/x = 1/x`
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