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 x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -arcsin({e}^{x}{\frac{1}{e}}^{x} - \frac{ln(\frac{(sqrt(1 - {e}^{(2x)}) + 1)}{(sqrt(1 - {e}^{(2x)}) - 1)})}{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -arcsin({e}^{x}{\frac{1}{e}}^{x} - \frac{1}{2}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -arcsin({e}^{x}{\frac{1}{e}}^{x} - \frac{1}{2}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}))\right)}{dx}\\=&-(\frac{(({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})){\frac{1}{e}}^{x} + {e}^{x}({\frac{1}{e}}^{x}((1)ln(\frac{1}{e}) + \frac{(x)(\frac{-0}{e^{2}})}{(\frac{1}{e})})) - \frac{\frac{1}{2}((\frac{-(\frac{(-({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 0)*\frac{1}{2}}{(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + 0)}{(sqrt(-{e}^{(2x)} + 1) - 1)^{2}})sqrt(-{e}^{(2x)} + 1) + \frac{(-({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 0)*\frac{1}{2}}{(sqrt(-{e}^{(2x)} + 1) - 1)(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + (\frac{-(\frac{(-({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 0)*\frac{1}{2}}{(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + 0)}{(sqrt(-{e}^{(2x)} + 1) - 1)^{2}}))}{(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})})}{((1 - ({e}^{x}{\frac{1}{e}}^{x} - \frac{1}{2}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}))^{2})^{\frac{1}{2}})})\\=&\frac{-{e}^{x}{\frac{1}{e}}^{x}}{(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}} + \frac{{\frac{1}{e}}^{x}{e}^{x}}{(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}} + \frac{{e}^{(2x)}sqrt(-{e}^{(2x)} + 1)}{2(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})(sqrt(-{e}^{(2x)} + 1) - 1)^{2}(-{e}^{(2x)} + 1)^{\frac{1}{2}}} - \frac{{e}^{(2x)}}{2(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})(sqrt(-{e}^{(2x)} + 1) - 1)(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + \frac{{e}^{(2x)}}{2(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})(sqrt(-{e}^{(2x)} + 1) - 1)^{2}(-{e}^{(2x)} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -arcsin({e}^{x}{\frac{1}{e}}^{x} - \frac{ln(\frac{(sqrt(1 - {e}^{(2x)}) + 1)}{(sqrt(1 - {e}^{(2x)}) - 1)})}{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -arcsin({e}^{x}{\frac{1}{e}}^{x} - \frac{1}{2}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -arcsin({e}^{x}{\frac{1}{e}}^{x} - \frac{1}{2}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}))\right)}{dx}\\=&-(\frac{(({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})){\frac{1}{e}}^{x} + {e}^{x}({\frac{1}{e}}^{x}((1)ln(\frac{1}{e}) + \frac{(x)(\frac{-0}{e^{2}})}{(\frac{1}{e})})) - \frac{\frac{1}{2}((\frac{-(\frac{(-({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 0)*\frac{1}{2}}{(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + 0)}{(sqrt(-{e}^{(2x)} + 1) - 1)^{2}})sqrt(-{e}^{(2x)} + 1) + \frac{(-({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 0)*\frac{1}{2}}{(sqrt(-{e}^{(2x)} + 1) - 1)(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + (\frac{-(\frac{(-({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 0)*\frac{1}{2}}{(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + 0)}{(sqrt(-{e}^{(2x)} + 1) - 1)^{2}}))}{(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})})}{((1 - ({e}^{x}{\frac{1}{e}}^{x} - \frac{1}{2}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}))^{2})^{\frac{1}{2}})})\\=&\frac{-{e}^{x}{\frac{1}{e}}^{x}}{(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}} + \frac{{\frac{1}{e}}^{x}{e}^{x}}{(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}} + \frac{{e}^{(2x)}sqrt(-{e}^{(2x)} + 1)}{2(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})(sqrt(-{e}^{(2x)} + 1) - 1)^{2}(-{e}^{(2x)} + 1)^{\frac{1}{2}}} - \frac{{e}^{(2x)}}{2(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})(sqrt(-{e}^{(2x)} + 1) - 1)(-{e}^{(2x)} + 1)^{\frac{1}{2}}} + \frac{{e}^{(2x)}}{2(\frac{1}{2}{e}^{x}{\frac{1}{e}}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + \frac{1}{2}{\frac{1}{e}}^{x}{e}^{x}ln(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) - {e}^{(2x)}{\frac{1}{e}}^{(2x)} - \frac{1}{4}ln^{2}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)}) + 1)^{\frac{1}{2}}(\frac{sqrt(-{e}^{(2x)} + 1)}{(sqrt(-{e}^{(2x)} + 1) - 1)} + \frac{1}{(sqrt(-{e}^{(2x)} + 1) - 1)})(sqrt(-{e}^{(2x)} + 1) - 1)^{2}(-{e}^{(2x)} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]