There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(-6sqrt(2)x + 144)}{(xx - 12sqrt(2)x + 144)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-6xsqrt(2)}{(-12xsqrt(2) + x^{2} + 144)} + \frac{144}{(-12xsqrt(2) + x^{2} + 144)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-6xsqrt(2)}{(-12xsqrt(2) + x^{2} + 144)} + \frac{144}{(-12xsqrt(2) + x^{2} + 144)}\right)}{dx}\\=&-6(\frac{-(-12sqrt(2) - 12x*0*\frac{1}{2}*2^{\frac{1}{2}} + 2x + 0)}{(-12xsqrt(2) + x^{2} + 144)^{2}})xsqrt(2) - \frac{6sqrt(2)}{(-12xsqrt(2) + x^{2} + 144)} - \frac{6x*0*\frac{1}{2}*2^{\frac{1}{2}}}{(-12xsqrt(2) + x^{2} + 144)} + 144(\frac{-(-12sqrt(2) - 12x*0*\frac{1}{2}*2^{\frac{1}{2}} + 2x + 0)}{(-12xsqrt(2) + x^{2} + 144)^{2}})\\=&\frac{-72xsqrt(2)^{2}}{(-12xsqrt(2) + x^{2} + 144)^{2}} + \frac{12x^{2}sqrt(2)}{(-12xsqrt(2) + x^{2} + 144)^{2}} - \frac{6sqrt(2)}{(-12xsqrt(2) + x^{2} + 144)} + \frac{1728sqrt(2)}{(-12xsqrt(2) + x^{2} + 144)^{2}} - \frac{288x}{(-12xsqrt(2) + x^{2} + 144)^{2}}\\ \end{split}\end{equation} \]

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