Solve d/dx(elnx-x/lnx(1-x))

$$\frac { d } { d x } ( \frac { e \ln x - x } { \ln x ( 1 - x ) } )$$

Evaluate

$$\frac{x^{2}\ln(x\left(1-x\right))-x\ln(x\left(1-x\right))-ex\ln(x\left(1-x\right))+e\ln(x\left(1-x\right))+2ex\ln(x)-e\ln(x)-2x^{2}+x}{x\left(1-x\right)\ln(x\left(1-x\right))^{2}}$$

Differentiate w.r.t. x

$$\frac{-e\left(x\ln(x\left(1-x\right))\right)^{2}+2ex\ln(x\left(1-x\right))^{2}+2ex^{2}\ln(x)\ln(x\left(1-x\right))+2x^{3}\ln(x\left(1-x\right))-e\ln(x\left(1-x\right))^{2}-2ex\ln(x)\ln(x\left(1-x\right))-4ex^{2}\ln(x\left(1-x\right))-4x^{2}\ln(x\left(1-x\right))+x\ln(x\left(1-x\right))+e\ln(x)\ln(x\left(1-x\right))+6ex\ln(x\left(1-x\right))-2e\ln(x\left(1-x\right))+8ex^{2}\ln(x)-8ex\ln(x)+2e\ln(x)-8x^{3}+8x^{2}-2x}{\left(x\left(1-x\right)\right)^{2}\ln(x\left(1-x\right))^{3}}$$