Initial program 60.1
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
Taylor expanded around 0 53.0
\[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]
- Using strategy
rm Applied add-log-exp53.1
\[\leadsto \left(x + \frac{2}{15} \cdot {x}^{5}\right) - \color{blue}{\log \left(e^{\frac{1}{3} \cdot {x}^{3}}\right)}\]
Taylor expanded around 0 53.0
\[\leadsto \left(x + \frac{2}{15} \cdot {x}^{5}\right) - \log \color{blue}{\left(\frac{1}{3} \cdot {x}^{3} + \left(\frac{1}{18} \cdot {x}^{6} + 1\right)\right)}\]
Taylor expanded around 0 53.0
\[\leadsto \left(x + \frac{2}{15} \cdot {x}^{5}\right) - \color{blue}{\left(\left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{648} \cdot {x}^{12}\right) - \frac{1}{162} \cdot {x}^{9}\right)}\]
Final simplification53.0
\[\leadsto \left(x + {x}^{5} \cdot \frac{2}{15}\right) - \left(\left({x}^{12} \cdot \frac{1}{648} + \frac{1}{3} \cdot {x}^{3}\right) - \frac{1}{162} \cdot {x}^{9}\right)\]
