Initial program 13.6
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
- Using strategy
rm Applied div-sub13.6
\[\leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
Applied associate--r-7.1
\[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
Taylor expanded around 0 1.1
\[\leadsto \color{blue}{\left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Simplified1.1
\[\leadsto \color{blue}{(wj \cdot \left(wj - wj \cdot wj\right) + \left({wj}^{4}\right))_*} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Taylor expanded around 0 1.5
\[\leadsto (wj \cdot \left(wj - wj \cdot wj\right) + \left({wj}^{4}\right))_* + \color{blue}{\left(\left(x + \frac{5}{2} \cdot \left(x \cdot {wj}^{2}\right)\right) - 2 \cdot \left(x \cdot wj\right)\right)}\]
Simplified1.5
\[\leadsto (wj \cdot \left(wj - wj \cdot wj\right) + \left({wj}^{4}\right))_* + \color{blue}{(\left(x \cdot wj\right) \cdot \left((wj \cdot \frac{5}{2} + -2)_*\right) + x)_*}\]
Final simplification1.5
\[\leadsto (wj \cdot \left(wj - wj \cdot wj\right) + \left({wj}^{4}\right))_* + (\left(wj \cdot x\right) \cdot \left((wj \cdot \frac{5}{2} + -2)_*\right) + x)_*\]
