Solve f(x)=x*lnx-a/2x^2

$$f ( x ) = x \cdot \ln x - \frac { a } { 2 } x ^ { 2 }$$

Factor

$$\frac{x\left(2\ln(x)-ax\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2x\log_{e}\left(x\right)-ax^{2}}{2}$$

Consider 2x\ln(x)\times \frac{1}{\ln(e)}-ax^{2}. Factor out x.

$$x\left(2\log_{e}\left(x\right)-ax\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(2\log_{e}\left(x\right)-ax\right)}{2}$$

Evaluate

$$x\ln(x)-\frac{ax^{2}}{2}$$