There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{30({x}^{2} - 2{x}^{3} + {x}^{4})}{(\frac{19}{10}sin(xpi))})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{300}{19}x^{2}}{sin(pix)} - \frac{\frac{600}{19}x^{3}}{sin(pix)} + \frac{\frac{300}{19}x^{4}}{sin(pix)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{300}{19}x^{2}}{sin(pix)} - \frac{\frac{600}{19}x^{3}}{sin(pix)} + \frac{\frac{300}{19}x^{4}}{sin(pix)}\right)}{dx}\\=&\frac{\frac{300}{19}*2x}{sin(pix)} + \frac{\frac{300}{19}x^{2}*-cos(pix)pi}{sin^{2}(pix)} - \frac{\frac{600}{19}*3x^{2}}{sin(pix)} - \frac{\frac{600}{19}x^{3}*-cos(pix)pi}{sin^{2}(pix)} + \frac{\frac{300}{19}*4x^{3}}{sin(pix)} + \frac{\frac{300}{19}x^{4}*-cos(pix)pi}{sin^{2}(pix)}\\=&\frac{600x}{19sin(pix)} - \frac{300pix^{2}cos(pix)}{19sin^{2}(pix)} - \frac{1800x^{2}}{19sin(pix)} + \frac{600pix^{3}cos(pix)}{19sin^{2}(pix)} + \frac{1200x^{3}}{19sin(pix)} - \frac{300pix^{4}cos(pix)}{19sin^{2}(pix)}\\ \end{split}\end{equation} \]

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