There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {x}^{2}(1 - {e}^{(\frac{(x - 1)}{a})})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - x^{2}{e}^{(\frac{x}{a} - \frac{1}{a})} + x^{2}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - x^{2}{e}^{(\frac{x}{a} - \frac{1}{a})} + x^{2}\right)}{dx}\\=& - 2x{e}^{(\frac{x}{a} - \frac{1}{a})} - x^{2}({e}^{(\frac{x}{a} - \frac{1}{a})}((\frac{1}{a} + 0)ln(e) + \frac{(\frac{x}{a} - \frac{1}{a})(0)}{(e)})) + 2x\\=& - 2x{e}^{(\frac{x}{a} - \frac{1}{a})} - \frac{x^{2}{e}^{(\frac{x}{a} - \frac{1}{a})}}{a} + 2x\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 2x{e}^{(\frac{x}{a} - \frac{1}{a})} - \frac{x^{2}{e}^{(\frac{x}{a} - \frac{1}{a})}}{a} + 2x\right)}{dx}\\=& - 2{e}^{(\frac{x}{a} - \frac{1}{a})} - 2x({e}^{(\frac{x}{a} - \frac{1}{a})}((\frac{1}{a} + 0)ln(e) + \frac{(\frac{x}{a} - \frac{1}{a})(0)}{(e)})) - \frac{2x{e}^{(\frac{x}{a} - \frac{1}{a})}}{a} - \frac{x^{2}({e}^{(\frac{x}{a} - \frac{1}{a})}((\frac{1}{a} + 0)ln(e) + \frac{(\frac{x}{a} - \frac{1}{a})(0)}{(e)}))}{a} + 2\\=& - 2{e}^{(\frac{x}{a} - \frac{1}{a})} - \frac{4x{e}^{(\frac{x}{a} - \frac{1}{a})}}{a} - \frac{x^{2}{e}^{(\frac{x}{a} - \frac{1}{a})}}{a^{2}} + 2\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !