Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 1 derivative of H is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{(bH - \frac{1}{2}(c({e}^{2}))(1 - {k}^{2}))(\frac{((1 - k)eS - rH)}{((1 - k)(eS - rH))})}{((1 - k)(bH - \frac{1}{2}(c({e}^{2}))(1 + k)))})\ with\ respect\ to\ H：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \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}{The\ first\ derivative\ function：}\\&\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} \]