There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{e^{\frac{-{(log_{10}^{x} - h)}^{2}}{(2{y}^{2})}}}{(sqrt(2t)xy)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yxsqrt(2t)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yxsqrt(2t)}\right)}{dx}\\=&\frac{-e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yx^{2}sqrt(2t)} + \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}(\frac{\frac{-1}{2}(\frac{2log_{10}^{x}(\frac{(1)}{(x)} - \frac{(0)log_{10}^{x}}{(10)})}{(ln(10))})}{y^{2}} + \frac{h(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{10}^{x}}{(10)})}{(ln(10))})}{y^{2}} + 0)}{yxsqrt(2t)} + \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}*-0*\frac{1}{2}}{yx(2t)(2t)^{\frac{1}{2}}}\\=&\frac{-e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yx^{2}sqrt(2t)} - \frac{log_{10}^{x}e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{y^{3}x^{2}ln(10)sqrt(2t)} + \frac{he^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{y^{3}x^{2}ln(10)sqrt(2t)}\\ \end{split}\end{equation} \]

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