If y = (x – 1)log (x – 1) – (x + 1) log (x +1), prove that .
Given y = (x – 1)log(x – 1) – (x + 1)log(x + 1)
On differentiating y with respect to x, we get
Recall that (uv)’ = vu’ + uv’ (product rule)
We know and.
Also, the derivative of a constant is 0.
Thus,