求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
本次共计算 1 个题目：每一题对 H 求 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{(bH - \frac{1}{2}(c({e}^{2}))(1 - {k}^{2}))(\frac{((1 - k)eS - rH)}{((1 - k)(eS - rH))})}{((1 - k)(bH - \frac{1}{2}(c({e}^{2}))(1 + k)))}) 关于 H 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-bkSHe}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{bSHe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} - \frac{brH^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}ck^{3}Se^{3}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}ck^{2}Se^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} - \frac{\frac{1}{2}ck^{2}rHe^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}ckSe^{3}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}cSe^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} + \frac{\frac{1}{2}crHe^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{-bkSHe}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{bSHe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} - \frac{brH^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}ck^{3}Se^{3}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}ck^{2}Se^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} - \frac{\frac{1}{2}ck^{2}rHe^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}ckSe^{3}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}cSe^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} + \frac{\frac{1}{2}crHe^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)}\right)}{dH}\\=&\frac{-(\frac{-2(0 + 0)}{(-k + 1)^{3}})bkSHe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})bkSHe}{(-k + 1)^{2}(Se - rH)} - \frac{(\frac{-(S*0 - r)}{(Se - rH)^{2}})bkSHe}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{bkSe}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{bkSH*0}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})bSHe}{(-k + 1)^{2}(Se - rH)} + \frac{(\frac{-2(0 + 0)}{(-k + 1)^{3}})bSHe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{(\frac{-(S*0 - r)}{(Se - rH)^{2}})bSHe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}} + \frac{bSe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} + \frac{bSH*0}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} - \frac{(\frac{-2(0 + 0)}{(-k + 1)^{3}})brH^{2}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})brH^{2}}{(-k + 1)^{2}(Se - rH)} - \frac{(\frac{-(S*0 - r)}{(Se - rH)^{2}})brH^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{br*2H}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}(\frac{-2(0 + 0)}{(-k + 1)^{3}})ck^{3}Se^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})ck^{3}Se^{3}}{(-k + 1)^{2}(Se - rH)} - \frac{\frac{1}{2}(\frac{-(S*0 - r)}{(Se - rH)^{2}})ck^{3}Se^{3}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{\frac{1}{2}ck^{3}S*3e^{2}*0}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})ck^{2}Se^{3}}{(-k + 1)^{2}(Se - rH)} + \frac{\frac{1}{2}(\frac{-2(0 + 0)}{(-k + 1)^{3}})ck^{2}Se^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}(\frac{-(S*0 - r)}{(Se - rH)^{2}})ck^{2}Se^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}} + \frac{\frac{1}{2}ck^{2}S*3e^{2}*0}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} - \frac{\frac{1}{2}(\frac{-2(0 + 0)}{(-k + 1)^{3}})ck^{2}rHe^{2}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})ck^{2}rHe^{2}}{(-k + 1)^{2}(Se - rH)} - \frac{\frac{1}{2}(\frac{-(S*0 - r)}{(Se - rH)^{2}})ck^{2}rHe^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{\frac{1}{2}ck^{2}re^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}ck^{2}rH*2e*0}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}(\frac{-2(0 + 0)}{(-k + 1)^{3}})ckSe^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})ckSe^{3}}{(-k + 1)^{2}(Se - rH)} + \frac{\frac{1}{2}(\frac{-(S*0 - r)}{(Se - rH)^{2}})ckSe^{3}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} + \frac{\frac{1}{2}ckS*3e^{2}*0}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})cSe^{3}}{(-k + 1)^{2}(Se - rH)} - \frac{\frac{1}{2}(\frac{-2(0 + 0)}{(-k + 1)^{3}})cSe^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{\frac{1}{2}(\frac{-(S*0 - r)}{(Se - rH)^{2}})cSe^{3}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}} - \frac{\frac{1}{2}cS*3e^{2}*0}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} + \frac{\frac{1}{2}(\frac{-2(0 + 0)}{(-k + 1)^{3}})crHe^{2}}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}(\frac{-(b - \frac{1}{2}ck*2e*0 - \frac{1}{2}c*2e*0)}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}})crHe^{2}}{(-k + 1)^{2}(Se - rH)} + \frac{\frac{1}{2}(\frac{-(S*0 - r)}{(Se - rH)^{2}})crHe^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} + \frac{\frac{1}{2}cre^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} + \frac{\frac{1}{2}crH*2e*0}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)}\\=&\frac{b^{2}kSHe}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(Se - rH)} + \frac{bkSrHe}{(-k + 1)^{2}(Se - rH)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{bkSe}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{b^{2}SHe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(-k + 1)^{2}(Se - rH)} + \frac{bSrHe}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)^{2}} + \frac{bSe}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(-k + 1)^{2}(Se - rH)} + \frac{b^{2}rH^{2}}{(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(Se - rH)} - \frac{br^{2}H^{2}}{(-k + 1)^{2}(Se - rH)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{2brH}{(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)(-k + 1)^{2}} + \frac{bck^{3}Se^{3}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(Se - rH)} - \frac{ck^{3}Sre^{3}}{2(-k + 1)^{2}(Se - rH)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{bck^{2}Se^{3}}{2(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(-k + 1)^{2}(Se - rH)} + \frac{ck^{2}Sre^{3}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)^{2}} + \frac{bck^{2}rHe^{2}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(Se - rH)} - \frac{ck^{2}r^{2}He^{2}}{2(-k + 1)^{2}(Se - rH)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} - \frac{ck^{2}re^{2}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)} - \frac{bckSe^{3}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(Se - rH)} + \frac{ckSre^{3}}{2(-k + 1)^{2}(Se - rH)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} + \frac{bcSe^{3}}{2(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(-k + 1)^{2}(Se - rH)} - \frac{cSre^{3}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)^{2}} - \frac{bcrHe^{2}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})^{2}(Se - rH)} + \frac{cr^{2}He^{2}}{2(-k + 1)^{2}(Se - rH)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})} + \frac{cre^{2}}{2(-k + 1)^{2}(bH - \frac{1}{2}cke^{2} - \frac{1}{2}ce^{2})(Se - rH)}\\ \end{split}\end{equation} \]
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