There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ th(e^{(ax) + xx - ax})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = th(e^{x^{2}})\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( th(e^{x^{2}})\right)}{dx}\\=&(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x\\=& - 2xe^{x^{2}}th^{2}(e^{x^{2}}) + 2xe^{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 2xe^{x^{2}}th^{2}(e^{x^{2}}) + 2xe^{x^{2}}\right)}{dx}\\=& - 2e^{x^{2}}th^{2}(e^{x^{2}}) - 2xe^{x^{2}}*2xth^{2}(e^{x^{2}}) - 2xe^{x^{2}}*2th(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x + 2e^{x^{2}} + 2xe^{x^{2}}*2x\\=& - 2e^{x^{2}}th^{2}(e^{x^{2}}) - 4x^{2}e^{x^{2}}th^{2}(e^{x^{2}}) - 8x^{2}e^{{x^{2}}*{2}}th(e^{x^{2}}) + 8x^{2}e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) + 2e^{x^{2}} + 4x^{2}e^{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 2e^{x^{2}}th^{2}(e^{x^{2}}) - 4x^{2}e^{x^{2}}th^{2}(e^{x^{2}}) - 8x^{2}e^{{x^{2}}*{2}}th(e^{x^{2}}) + 8x^{2}e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) + 2e^{x^{2}} + 4x^{2}e^{x^{2}}\right)}{dx}\\=& - 2e^{x^{2}}*2xth^{2}(e^{x^{2}}) - 2e^{x^{2}}*2th(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x - 4*2xe^{x^{2}}th^{2}(e^{x^{2}}) - 4x^{2}e^{x^{2}}*2xth^{2}(e^{x^{2}}) - 4x^{2}e^{x^{2}}*2th(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x - 8*2xe^{{x^{2}}*{2}}th(e^{x^{2}}) - 8x^{2}*2e^{x^{2}}e^{x^{2}}*2xth(e^{x^{2}}) - 8x^{2}e^{{x^{2}}*{2}}(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x + 8*2xe^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) + 8x^{2}*2e^{x^{2}}e^{x^{2}}*2xth^{3}(e^{x^{2}}) + 8x^{2}e^{{x^{2}}*{2}}*3th^{2}(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x + 2e^{x^{2}}*2x + 4*2xe^{x^{2}} + 4x^{2}e^{x^{2}}*2x\\=& - 12xe^{x^{2}}th^{2}(e^{x^{2}}) - 24xe^{{x^{2}}*{2}}th(e^{x^{2}}) + 24xe^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) - 8x^{3}e^{x^{2}}th^{2}(e^{x^{2}}) - 48x^{3}e^{{x^{2}}*{2}}th(e^{x^{2}}) + 48x^{3}e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) + 64x^{3}e^{{x^{2}}*{3}}th^{2}(e^{x^{2}}) - 48x^{3}e^{{x^{2}}*{3}}th^{4}(e^{x^{2}}) - 16x^{3}e^{{x^{2}}*{3}} + 12xe^{x^{2}} + 8x^{3}e^{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 12xe^{x^{2}}th^{2}(e^{x^{2}}) - 24xe^{{x^{2}}*{2}}th(e^{x^{2}}) + 24xe^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) - 8x^{3}e^{x^{2}}th^{2}(e^{x^{2}}) - 48x^{3}e^{{x^{2}}*{2}}th(e^{x^{2}}) + 48x^{3}e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) + 64x^{3}e^{{x^{2}}*{3}}th^{2}(e^{x^{2}}) - 48x^{3}e^{{x^{2}}*{3}}th^{4}(e^{x^{2}}) - 16x^{3}e^{{x^{2}}*{3}} + 12xe^{x^{2}} + 8x^{3}e^{x^{2}}\right)}{dx}\\=& - 12e^{x^{2}}th^{2}(e^{x^{2}}) - 12xe^{x^{2}}*2xth^{2}(e^{x^{2}}) - 12xe^{x^{2}}*2th(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x - 24e^{{x^{2}}*{2}}th(e^{x^{2}}) - 24x*2e^{x^{2}}e^{x^{2}}*2xth(e^{x^{2}}) - 24xe^{{x^{2}}*{2}}(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x + 24e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) + 24x*2e^{x^{2}}e^{x^{2}}*2xth^{3}(e^{x^{2}}) + 24xe^{{x^{2}}*{2}}*3th^{2}(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x - 8*3x^{2}e^{x^{2}}th^{2}(e^{x^{2}}) - 8x^{3}e^{x^{2}}*2xth^{2}(e^{x^{2}}) - 8x^{3}e^{x^{2}}*2th(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x - 48*3x^{2}e^{{x^{2}}*{2}}th(e^{x^{2}}) - 48x^{3}*2e^{x^{2}}e^{x^{2}}*2xth(e^{x^{2}}) - 48x^{3}e^{{x^{2}}*{2}}(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x + 48*3x^{2}e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) + 48x^{3}*2e^{x^{2}}e^{x^{2}}*2xth^{3}(e^{x^{2}}) + 48x^{3}e^{{x^{2}}*{2}}*3th^{2}(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x + 64*3x^{2}e^{{x^{2}}*{3}}th^{2}(e^{x^{2}}) + 64x^{3}*3e^{{x^{2}}*{2}}e^{x^{2}}*2xth^{2}(e^{x^{2}}) + 64x^{3}e^{{x^{2}}*{3}}*2th(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x - 48*3x^{2}e^{{x^{2}}*{3}}th^{4}(e^{x^{2}}) - 48x^{3}*3e^{{x^{2}}*{2}}e^{x^{2}}*2xth^{4}(e^{x^{2}}) - 48x^{3}e^{{x^{2}}*{3}}*4th^{3}(e^{x^{2}})(1 - th^{2}(e^{x^{2}}))e^{x^{2}}*2x - 16*3x^{2}e^{{x^{2}}*{3}} - 16x^{3}*3e^{{x^{2}}*{2}}e^{x^{2}}*2x + 12e^{x^{2}} + 12xe^{x^{2}}*2x + 8*3x^{2}e^{x^{2}} + 8x^{3}e^{x^{2}}*2x\\=& - 12e^{x^{2}}th^{2}(e^{x^{2}}) - 48x^{2}e^{x^{2}}th^{2}(e^{x^{2}}) - 288x^{2}e^{{x^{2}}*{2}}th(e^{x^{2}}) + 288x^{2}e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) - 24e^{{x^{2}}*{2}}th(e^{x^{2}}) + 384x^{2}e^{{x^{2}}*{3}}th^{2}(e^{x^{2}}) - 288x^{2}e^{{x^{2}}*{3}}th^{4}(e^{x^{2}}) + 24e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) - 224x^{4}e^{{x^{2}}*{2}}th(e^{x^{2}}) + 224x^{4}e^{{x^{2}}*{2}}th^{3}(e^{x^{2}}) - 16x^{4}e^{x^{2}}th^{2}(e^{x^{2}}) + 768x^{4}e^{{x^{2}}*{3}}th^{2}(e^{x^{2}}) - 576x^{4}e^{{x^{2}}*{3}}th^{4}(e^{x^{2}}) + 256x^{4}e^{{x^{2}}*{4}}th(e^{x^{2}}) - 640x^{4}e^{{x^{2}}*{4}}th^{3}(e^{x^{2}}) + 384x^{4}e^{{x^{2}}*{4}}th^{5}(e^{x^{2}}) - 192x^{4}e^{{x^{2}}*{3}} - 96x^{2}e^{{x^{2}}*{3}} + 12e^{x^{2}} + 48x^{2}e^{x^{2}} + 16x^{4}e^{x^{2}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !