There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {\frac{1}{2}}^{x} + 1\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {\frac{1}{2}}^{x} + 1\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})})) + 0\\=&{\frac{1}{2}}^{x}ln(\frac{1}{2})\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {\frac{1}{2}}^{x}ln(\frac{1}{2})\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2}) + \frac{{\frac{1}{2}}^{x}*0}{(\frac{1}{2})}\\=&{\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln^{2}(\frac{1}{2}) + \frac{{\frac{1}{2}}^{x}*2ln(\frac{1}{2})*0}{(\frac{1}{2})}\\=&{\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( {\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln^{3}(\frac{1}{2}) + \frac{{\frac{1}{2}}^{x}*3ln^{2}(\frac{1}{2})*0}{(\frac{1}{2})}\\=&{\frac{1}{2}}^{x}ln^{4}(\frac{1}{2})\\ \end{split}\end{equation} \]

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