There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {((x + 1){(2x - 1)}^{2}{\frac{1}{(4 - 3x)}}^{5})}^{\frac{1}{3}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{1}{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{1}{3}}\right)}{dx}\\=&(\frac{\frac{1}{3}(4(\frac{-5(-3 + 0)}{(-3x + 4)^{6}})x^{3} + \frac{4*3x^{2}}{(-3x + 4)^{5}} - 3(\frac{-5(-3 + 0)}{(-3x + 4)^{6}})x - \frac{3}{(-3x + 4)^{5}} + (\frac{-5(-3 + 0)}{(-3x + 4)^{6}}))}{(\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{2}{3}}})\\=&\frac{20x^{3}}{(\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{2}{3}}(-3x + 4)^{6}} + \frac{4x^{2}}{(\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{2}{3}}(-3x + 4)^{5}} - \frac{15x}{(\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{2}{3}}(-3x + 4)^{6}} - \frac{1}{(\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{2}{3}}(-3x + 4)^{5}} + \frac{5}{(\frac{4x^{3}}{(-3x + 4)^{5}} - \frac{3x}{(-3x + 4)^{5}} + \frac{1}{(-3x + 4)^{5}})^{\frac{2}{3}}(-3x + 4)^{6}}\\ \end{split}\end{equation} \]

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