There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(({x}^{2} + sqrt(3)x + \frac{3}{4})(36 - {x}^{2} + x - \frac{1}{4}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})\right)}{dx}\\=&\frac{(-3x^{2}sqrt(3) - x^{3}*0*\frac{1}{2}*3^{\frac{1}{2}} + \frac{143}{4}sqrt(3) + \frac{143}{4}x*0*\frac{1}{2}*3^{\frac{1}{2}} + 2xsqrt(3) + x^{2}*0*\frac{1}{2}*3^{\frac{1}{2}} - 4x^{3} + 3x^{2} + 35*2x + \frac{3}{4} + 0)*\frac{1}{2}}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}}\\=&\frac{-3x^{2}sqrt(3)}{2(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{143sqrt(3)}{8(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{xsqrt(3)}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} - \frac{2x^{3}}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{3x^{2}}{2(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{35x}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{3}{8(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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