There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ ln(55{x}^{2} + 38x - 90)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(55x^{2} + 38x - 90)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(55x^{2} + 38x - 90)\right)}{dx}\\=&\frac{(55*2x + 38 + 0)}{(55x^{2} + 38x - 90)}\\=&\frac{110x}{(55x^{2} + 38x - 90)} + \frac{38}{(55x^{2} + 38x - 90)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{110x}{(55x^{2} + 38x - 90)} + \frac{38}{(55x^{2} + 38x - 90)}\right)}{dx}\\=&110(\frac{-(55*2x + 38 + 0)}{(55x^{2} + 38x - 90)^{2}})x + \frac{110}{(55x^{2} + 38x - 90)} + 38(\frac{-(55*2x + 38 + 0)}{(55x^{2} + 38x - 90)^{2}})\\=&\frac{-12100x^{2}}{(55x^{2} + 38x - 90)^{2}} - \frac{8360x}{(55x^{2} + 38x - 90)^{2}} + \frac{110}{(55x^{2} + 38x - 90)} - \frac{1444}{(55x^{2} + 38x - 90)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-12100x^{2}}{(55x^{2} + 38x - 90)^{2}} - \frac{8360x}{(55x^{2} + 38x - 90)^{2}} + \frac{110}{(55x^{2} + 38x - 90)} - \frac{1444}{(55x^{2} + 38x - 90)^{2}}\right)}{dx}\\=&-12100(\frac{-2(55*2x + 38 + 0)}{(55x^{2} + 38x - 90)^{3}})x^{2} - \frac{12100*2x}{(55x^{2} + 38x - 90)^{2}} - 8360(\frac{-2(55*2x + 38 + 0)}{(55x^{2} + 38x - 90)^{3}})x - \frac{8360}{(55x^{2} + 38x - 90)^{2}} + 110(\frac{-(55*2x + 38 + 0)}{(55x^{2} + 38x - 90)^{2}}) - 1444(\frac{-2(55*2x + 38 + 0)}{(55x^{2} + 38x - 90)^{3}})\\=&\frac{2662000x^{3}}{(55x^{2} + 38x - 90)^{3}} + \frac{2758800x^{2}}{(55x^{2} + 38x - 90)^{3}} - \frac{36300x}{(55x^{2} + 38x - 90)^{2}} + \frac{953040x}{(55x^{2} + 38x - 90)^{3}} - \frac{12540}{(55x^{2} + 38x - 90)^{2}} + \frac{109744}{(55x^{2} + 38x - 90)^{3}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！