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

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