There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(2t(t - 1)x(x - sqrt({t}^{2} - 49)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(-2t^{2}xsqrt(t^{2} - 49) + 2txsqrt(t^{2} - 49) - 2tx^{2} + 2t^{2}x^{2})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(-2t^{2}xsqrt(t^{2} - 49) + 2txsqrt(t^{2} - 49) - 2tx^{2} + 2t^{2}x^{2})\right)}{dx}\\=&\frac{(-2t^{2}sqrt(t^{2} - 49) - \frac{2t^{2}x(0 + 0)*\frac{1}{2}}{(t^{2} - 49)^{\frac{1}{2}}} + 2tsqrt(t^{2} - 49) + \frac{2tx(0 + 0)*\frac{1}{2}}{(t^{2} - 49)^{\frac{1}{2}}} - 2t*2x + 2t^{2}*2x)*\frac{1}{2}}{(-2t^{2}xsqrt(t^{2} - 49) + 2txsqrt(t^{2} - 49) - 2tx^{2} + 2t^{2}x^{2})^{\frac{1}{2}}}\\=&\frac{-t^{2}sqrt(t^{2} - 49)}{(-2t^{2}xsqrt(t^{2} - 49) + 2txsqrt(t^{2} - 49) - 2tx^{2} + 2t^{2}x^{2})^{\frac{1}{2}}} + \frac{tsqrt(t^{2} - 49)}{(-2t^{2}xsqrt(t^{2} - 49) + 2txsqrt(t^{2} - 49) - 2tx^{2} + 2t^{2}x^{2})^{\frac{1}{2}}} - \frac{2tx}{(-2t^{2}xsqrt(t^{2} - 49) + 2txsqrt(t^{2} - 49) - 2tx^{2} + 2t^{2}x^{2})^{\frac{1}{2}}} + \frac{2t^{2}x}{(-2t^{2}xsqrt(t^{2} - 49) + 2txsqrt(t^{2} - 49) - 2tx^{2} + 2t^{2}x^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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