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 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ th(e^{-sqrt(9 - {x}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = th(e^{-sqrt(-x^{2} + 9)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( th(e^{-sqrt(-x^{2} + 9)})\right)}{dx}\\=&\frac{(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{1}{2}}}\\=& - \frac{xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{1}{2}}} + \frac{xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{1}{2}}} + \frac{xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{1}{2}}}\right)}{dx}\\=& - (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{3}{2}}})xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{1}{2}}} - \frac{xe^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{1}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{xe^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{1}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{3}{2}}})xe^{-sqrt(-x^{2} + 9)} + \frac{e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{1}{2}}} + \frac{xe^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{1}{2}}(-x^{2} + 9)^{\frac{1}{2}}}\\=& - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{1}{2}}} - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{2x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{2x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{1}{2}}} + \frac{x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{1}{2}}} - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{2x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{2x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{1}{2}}} + \frac{x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)}\right)}{dx}\\=& - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{2xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{3}{2}}})e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{1}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{e^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{1}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - (\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{2xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} - \frac{x^{2}e^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} - 2(\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)}) - \frac{2*2xe^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{2x^{2}*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} - \frac{2x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} + 2(\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)}) + \frac{2*2xe^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{2x^{2}*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} + \frac{2x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}*3th^{2}(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{2}e^{-sqrt(-x^{2} + 9)} + \frac{2xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{x^{2}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{3}{2}}})e^{-sqrt(-x^{2} + 9)} + \frac{e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{1}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + (\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})x^{2}e^{-sqrt(-x^{2} + 9)} + \frac{2xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)} + \frac{x^{2}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}}\\=& - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{3xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{3xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{6xe^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{6xe^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{8x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{4}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{2x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{5}{2}}} + \frac{3xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{2}} + \frac{3xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)} + \frac{x^{3}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{3xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{3xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{6xe^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{6xe^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{8x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{4}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{2x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{5}{2}}} + \frac{3xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{2}} + \frac{3xe^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)} + \frac{x^{3}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}}\right)}{dx}\\=& - 3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{7}{2}}})x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{3*3x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{5}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - 3(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{3e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{3xe^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{3xe^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - 3(\frac{-2(-2x + 0)}{(-x^{2} + 9)^{3}})x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{3*3x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{2}(-x^{2} + 9)^{\frac{1}{2}}} - 6(\frac{-2(-2x + 0)}{(-x^{2} + 9)^{3}})x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)}) - \frac{6*3x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{6x^{3}*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{2}(-x^{2} + 9)^{\frac{1}{2}}} + 6(\frac{-2(-2x + 0)}{(-x^{2} + 9)^{3}})x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)}) + \frac{6*3x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{6x^{3}*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}(-x^{2} + 9)^{\frac{1}{2}}} + \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}*3th^{2}(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{2}(-x^{2} + 9)^{\frac{1}{2}}} - 3(\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})xe^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{3e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{3xe^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} - \frac{3xe^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} - 6(\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})xe^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)}) - \frac{6e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{6x*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} - \frac{6xe^{{-sqrt(-x^{2} + 9)}*{2}}(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} + 6(\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})xe^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)}) + \frac{6e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{6x*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} + \frac{6xe^{{-sqrt(-x^{2} + 9)}*{2}}*3th^{2}(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{3}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)}) - \frac{3x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{x^{3}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{x^{3}e^{-sqrt(-x^{2} + 9)}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - 6(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)}) - \frac{6*3x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{6x^{3}*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + 6(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)}) + \frac{6*3x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{6x^{3}*2e^{-sqrt(-x^{2} + 9)}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{2}}*3th^{2}(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + 8(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{2}(e^{-sqrt(-x^{2} + 9)}) + \frac{8*3x^{2}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{8x^{3}*3e^{{-sqrt(-x^{2} + 9)}*{2}}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + \frac{8x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}*2th(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - 6(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{4}(e^{-sqrt(-x^{2} + 9)}) - \frac{6*3x^{2}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{4}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{6x^{3}*3e^{{-sqrt(-x^{2} + 9)}*{2}}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}th^{4}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - \frac{6x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}}*4th^{3}(e^{-sqrt(-x^{2} + 9)})(1 - th^{2}(e^{-sqrt(-x^{2} + 9)}))e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} - 2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{3}e^{{-sqrt(-x^{2} + 9)}*{3}} - \frac{2*3x^{2}e^{{-sqrt(-x^{2} + 9)}*{3}}}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{2x^{3}*3e^{{-sqrt(-x^{2} + 9)}*{2}}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + 3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{7}{2}}})x^{3}e^{-sqrt(-x^{2} + 9)} + \frac{3*3x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{5}{2}}} + \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{5}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + 3(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})xe^{-sqrt(-x^{2} + 9)} + \frac{3e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{3xe^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}} + 3(\frac{-2(-2x + 0)}{(-x^{2} + 9)^{3}})x^{3}e^{-sqrt(-x^{2} + 9)} + \frac{3*3x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{2}} + \frac{3x^{3}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{2}(-x^{2} + 9)^{\frac{1}{2}}} + 3(\frac{-(-2x + 0)}{(-x^{2} + 9)^{2}})xe^{-sqrt(-x^{2} + 9)} + \frac{3e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)} + \frac{3xe^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 9)^{\frac{5}{2}}})x^{3}e^{-sqrt(-x^{2} + 9)} + \frac{3x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{x^{3}e^{-sqrt(-x^{2} + 9)}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)^{\frac{3}{2}}(-x^{2} + 9)^{\frac{1}{2}}}\\=& - \frac{15x^{4}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{7}{2}}} - \frac{18x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{15x^{4}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{3}} - \frac{30x^{4}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{3}} + \frac{30x^{4}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{3}} - \frac{3e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{18x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{36x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{36x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{6x^{4}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{36x^{4}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} + \frac{36x^{4}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} + \frac{48x^{4}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{36x^{4}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{4}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{36x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{36x^{2}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{3e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{6x^{2}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{48x^{2}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{36x^{2}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{4}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{6e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} - \frac{14x^{4}e^{{-sqrt(-x^{2} + 9)}*{2}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{14x^{4}e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{6e^{{-sqrt(-x^{2} + 9)}*{2}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)} + \frac{48x^{4}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{36x^{4}e^{{-sqrt(-x^{2} + 9)}*{3}}th^{4}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{x^{4}e^{-sqrt(-x^{2} + 9)}th^{2}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{16x^{4}e^{{-sqrt(-x^{2} + 9)}*{4}}th(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{40x^{4}e^{{-sqrt(-x^{2} + 9)}*{4}}th^{3}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} + \frac{24x^{4}e^{{-sqrt(-x^{2} + 9)}*{4}}th^{5}(e^{-sqrt(-x^{2} + 9)})}{(-x^{2} + 9)^{2}} - \frac{12x^{4}e^{{-sqrt(-x^{2} + 9)}*{3}}}{(-x^{2} + 9)^{\frac{5}{2}}} - \frac{12x^{2}e^{{-sqrt(-x^{2} + 9)}*{3}}}{(-x^{2} + 9)^{\frac{3}{2}}} - \frac{12x^{4}e^{{-sqrt(-x^{2} + 9)}*{3}}}{(-x^{2} + 9)^{2}} + \frac{15x^{4}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{7}{2}}} + \frac{18x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{5}{2}}} + \frac{15x^{4}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{3}} + \frac{3e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{18x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{2}} + \frac{6x^{4}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{5}{2}}} + \frac{3e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)} + \frac{6x^{2}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{\frac{3}{2}}} + \frac{x^{4}e^{-sqrt(-x^{2} + 9)}}{(-x^{2} + 9)^{2}}\\ \end{split}\end{equation} \]