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

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