\(\frac{\frac{\sqrt{e^{x}}}{x}}{{\left(e^{\frac{1}{24}}\right)}^{\left({x}^2\right)}}\)
- Started with
\[\frac{e^{x}}{e^{x} - 1}\]
18.8
- Using strategy
rm 18.8
- Applied add-exp-log to get
\[\frac{e^{x}}{\color{red}{e^{x} - 1}} \leadsto \frac{e^{x}}{\color{blue}{e^{\log \left(e^{x} - 1\right)}}}\]
29.2
- Applied div-exp to get
\[\color{red}{\frac{e^{x}}{e^{\log \left(e^{x} - 1\right)}}} \leadsto \color{blue}{e^{x - \log \left(e^{x} - 1\right)}}\]
27.6
- Applied taylor to get
\[e^{x - \log \left(e^{x} - 1\right)} \leadsto e^{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)}\]
20.5
- Taylor expanded around 0 to get
\[e^{\color{red}{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)}} \leadsto e^{\color{blue}{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)}}\]
20.5
- Applied simplify to get
\[e^{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)} \leadsto \frac{\frac{\sqrt{e^{x}}}{{\left(e^{\frac{1}{24}}\right)}^{\left(x \cdot x\right)}}}{x}\]
1.8
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{\frac{\sqrt{e^{x}}}{{\left(e^{\frac{1}{24}}\right)}^{\left(x \cdot x\right)}}}{x}} \leadsto \color{blue}{\frac{\frac{\sqrt{e^{x}}}{x}}{{\left(e^{\frac{1}{24}}\right)}^{\left({x}^2\right)}}}\]
1.8
