\((wj * \left(wj - {wj}^2\right) + \left({wj}^{4}\right))_* + \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\)
- Started with
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
18.8
- Using strategy
rm 18.8
- Applied div-sub to get
\[wj - \color{red}{\frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}} \leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
18.8
- Applied associate--r- to get
\[\color{red}{wj - \left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)} \leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
13.4
- Applied simplify to get
\[\color{red}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}} \leadsto \color{blue}{\left(wj - \frac{wj}{1 + wj}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
13.4
- Applied taylor to get
\[\left(wj - \frac{wj}{1 + wj}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}} \leadsto \left(\left({wj}^{4} + {wj}^2\right) - {wj}^{3}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
0.0
- Taylor expanded around 0 to get
\[\color{red}{\left(\left({wj}^{4} + {wj}^2\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}} \leadsto \color{blue}{\left(\left({wj}^{4} + {wj}^2\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
0.0
- Applied simplify to get
\[\color{red}{\left(\left({wj}^{4} + {wj}^2\right) - {wj}^{3}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}} \leadsto \color{blue}{(wj * \left(wj - {wj}^2\right) + \left({wj}^{4}\right))_* + \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}}\]
0.0
