There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{\frac{1}{2}} + 6)}{(-{x}^{3} + 35x)}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{\frac{1}{2}}}{(-x^{3} + 35x)} + \frac{6}{(-x^{3} + 35x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{\frac{1}{2}}}{(-x^{3} + 35x)} + \frac{6}{(-x^{3} + 35x)}\right)}{dt}\\=&(\frac{-(0 + 0)}{(-x^{3} + 35x)^{2}})x^{\frac{1}{2}} + 0 + 6(\frac{-(0 + 0)}{(-x^{3} + 35x)^{2}})\\=& - 0\\ \end{split}\end{equation} \]

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