There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {{2}^{x}}^{(x - a)}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( {{2}^{x}}^{(x - a)}\right)}{dx}\\=&({{2}^{x}}^{(x - a)}((1 + 0)ln({2}^{x}) + \frac{(x - a)(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{({2}^{x})}))\\=&{{2}^{x}}^{(x - a)}ln({2}^{x}) + x{{2}^{x}}^{(x - a)}ln(2) - a{{2}^{x}}^{(x - a)}ln(2)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {{2}^{x}}^{(x - a)}ln({2}^{x}) + x{{2}^{x}}^{(x - a)}ln(2) - a{{2}^{x}}^{(x - a)}ln(2)\right)}{dx}\\=&({{2}^{x}}^{(x - a)}((1 + 0)ln({2}^{x}) + \frac{(x - a)(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{({2}^{x})}))ln({2}^{x}) + \frac{{{2}^{x}}^{(x - a)}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{({2}^{x})} + {{2}^{x}}^{(x - a)}ln(2) + x({{2}^{x}}^{(x - a)}((1 + 0)ln({2}^{x}) + \frac{(x - a)(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{({2}^{x})}))ln(2) + \frac{x{{2}^{x}}^{(x - a)}*0}{(2)} - a({{2}^{x}}^{(x - a)}((1 + 0)ln({2}^{x}) + \frac{(x - a)(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{({2}^{x})}))ln(2) - \frac{a{{2}^{x}}^{(x - a)}*0}{(2)}\\=&{{2}^{x}}^{(x - a)}ln^{2}({2}^{x}) + x{{2}^{x}}^{(x - a)}ln(2)ln({2}^{x}) - a{{2}^{x}}^{(x - a)}ln(2)ln({2}^{x}) + 2{{2}^{x}}^{(x - a)}ln(2) + x{{2}^{x}}^{(x - a)}ln({2}^{x})ln(2) + x^{2}{{2}^{x}}^{(x - a)}ln^{2}(2) - 2ax{{2}^{x}}^{(x - a)}ln^{2}(2) - a{{2}^{x}}^{(x - a)}ln({2}^{x})ln(2) + a^{2}{{2}^{x}}^{(x - a)}ln^{2}(2)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !