d/dx(xlogx/(x-1))

asked by guest
on Feb 02, 2025 at 10:27 am



You asked:

Evaluate the expression: ddx[xlog⁡(x)x−1]\frac{d}{dx}\left[\frac{x \log\left( x \right)}{x - 1}\right]

MathBot Answer:

Evaluated



ddx[xlog⁡(x)x−1]=−xlog⁡(x)(x−1)2+log⁡(x)x−1+1x−1\displaystyle \frac{d}{dx}\left[\frac{x \log\left( x \right)}{x - 1}\right] = - \frac{x \log{\left(x \right)}}{\left(x - 1\right)^{2}} + \frac{\log{\left(x \right)}}{x - 1} + \frac{1}{x - 1}

Expanded

ddx[xlog⁡(x)x−1]=ddxxlog⁡(x)x−1\frac{d}{dx}\left[\frac{x \log\left( x \right)}{x - 1}\right] = \frac{d}{d x} \frac{x \log{\left(x \right)}}{x - 1}

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