本次共计算 1 个题目:每一题对 x 求 1 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数\frac{e^{\frac{-{(log_{10}^{x} - h)}^{2}}{(2{y}^{2})}}}{(sqrt(2t)xy)} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yxsqrt(2t)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yxsqrt(2t)}\right)}{dx}\\=&\frac{-e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yx^{2}sqrt(2t)} + \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}(\frac{\frac{-1}{2}(\frac{2log_{10}^{x}(\frac{(1)}{(x)} - \frac{(0)log_{10}^{x}}{(10)})}{(ln(10))})}{y^{2}} + \frac{h(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{10}^{x}}{(10)})}{(ln(10))})}{y^{2}} + 0)}{yxsqrt(2t)} + \frac{e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}*-0*\frac{1}{2}}{yx(2t)(2t)^{\frac{1}{2}}}\\=&\frac{-e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{yx^{2}sqrt(2t)} - \frac{log_{10}^{x}e^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{y^{3}x^{2}ln(10)sqrt(2t)} + \frac{he^{\frac{\frac{-1}{2}{\left(log_{10}^{x}\right)}^{2}}{y^{2}} + \frac{hlog_{10}^{x}}{y^{2}} - \frac{\frac{1}{2}h^{2}}{y^{2}}}}{y^{3}x^{2}ln(10)sqrt(2t)}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!