There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (sin(x) + 1)({x}^{2} - cos(x) - e^{x})e^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}e^{x}sin(x) - e^{x}sin(x)cos(x) - e^{{x}*{2}}sin(x) + x^{2}e^{x} - e^{x}cos(x) - e^{{x}*{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}e^{x}sin(x) - e^{x}sin(x)cos(x) - e^{{x}*{2}}sin(x) + x^{2}e^{x} - e^{x}cos(x) - e^{{x}*{2}}\right)}{dx}\\=&2xe^{x}sin(x) + x^{2}e^{x}sin(x) + x^{2}e^{x}cos(x) - e^{x}sin(x)cos(x) - e^{x}cos(x)cos(x) - e^{x}sin(x)*-sin(x) - 2e^{x}e^{x}sin(x) - e^{{x}*{2}}cos(x) + 2xe^{x} + x^{2}e^{x} - e^{x}cos(x) - e^{x}*-sin(x) - 2e^{x}e^{x}\\=&2xe^{x}sin(x) + x^{2}e^{x}sin(x) + x^{2}e^{x}cos(x) - e^{x}sin(x)cos(x) - e^{x}cos^{2}(x) + e^{x}sin^{2}(x) - 2e^{{x}*{2}}sin(x) - e^{{x}*{2}}cos(x) + 2xe^{x} + x^{2}e^{x} - e^{x}cos(x) + e^{x}sin(x) - 2e^{{x}*{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2xe^{x}sin(x) + x^{2}e^{x}sin(x) + x^{2}e^{x}cos(x) - e^{x}sin(x)cos(x) - e^{x}cos^{2}(x) + e^{x}sin^{2}(x) - 2e^{{x}*{2}}sin(x) - e^{{x}*{2}}cos(x) + 2xe^{x} + x^{2}e^{x} - e^{x}cos(x) + e^{x}sin(x) - 2e^{{x}*{2}}\right)}{dx}\\=&2e^{x}sin(x) + 2xe^{x}sin(x) + 2xe^{x}cos(x) + 2xe^{x}sin(x) + x^{2}e^{x}sin(x) + x^{2}e^{x}cos(x) + 2xe^{x}cos(x) + x^{2}e^{x}cos(x) + x^{2}e^{x}*-sin(x) - e^{x}sin(x)cos(x) - e^{x}cos(x)cos(x) - e^{x}sin(x)*-sin(x) - e^{x}cos^{2}(x) - e^{x}*-2cos(x)sin(x) + e^{x}sin^{2}(x) + e^{x}*2sin(x)cos(x) - 2*2e^{x}e^{x}sin(x) - 2e^{{x}*{2}}cos(x) - 2e^{x}e^{x}cos(x) - e^{{x}*{2}}*-sin(x) + 2e^{x} + 2xe^{x} + 2xe^{x} + x^{2}e^{x} - e^{x}cos(x) - e^{x}*-sin(x) + e^{x}sin(x) + e^{x}cos(x) - 2*2e^{x}e^{x}\\=&3e^{x}sin(x)cos(x) + 4xe^{x}sin(x) + 4xe^{x}cos(x) + 2x^{2}e^{x}cos(x) + 4e^{x}sin(x) - 2e^{x}cos^{2}(x) + 2e^{x}sin^{2}(x) - 3e^{{x}*{2}}sin(x) - 4e^{{x}*{2}}cos(x) + 2e^{x} + 4xe^{x} + x^{2}e^{x} - 4e^{{x}*{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 3e^{x}sin(x)cos(x) + 4xe^{x}sin(x) + 4xe^{x}cos(x) + 2x^{2}e^{x}cos(x) + 4e^{x}sin(x) - 2e^{x}cos^{2}(x) + 2e^{x}sin^{2}(x) - 3e^{{x}*{2}}sin(x) - 4e^{{x}*{2}}cos(x) + 2e^{x} + 4xe^{x} + x^{2}e^{x} - 4e^{{x}*{2}}\right)}{dx}\\=&3e^{x}sin(x)cos(x) + 3e^{x}cos(x)cos(x) + 3e^{x}sin(x)*-sin(x) + 4e^{x}sin(x) + 4xe^{x}sin(x) + 4xe^{x}cos(x) + 4e^{x}cos(x) + 4xe^{x}cos(x) + 4xe^{x}*-sin(x) + 2*2xe^{x}cos(x) + 2x^{2}e^{x}cos(x) + 2x^{2}e^{x}*-sin(x) + 4e^{x}sin(x) + 4e^{x}cos(x) - 2e^{x}cos^{2}(x) - 2e^{x}*-2cos(x)sin(x) + 2e^{x}sin^{2}(x) + 2e^{x}*2sin(x)cos(x) - 3*2e^{x}e^{x}sin(x) - 3e^{{x}*{2}}cos(x) - 4*2e^{x}e^{x}cos(x) - 4e^{{x}*{2}}*-sin(x) + 2e^{x} + 4e^{x} + 4xe^{x} + 2xe^{x} + x^{2}e^{x} - 4*2e^{x}e^{x}\\=&11e^{x}sin(x)cos(x) + e^{x}cos^{2}(x) - e^{x}sin^{2}(x) + 8e^{x}sin(x) + 12xe^{x}cos(x) + 8e^{x}cos(x) + 2x^{2}e^{x}cos(x) - 2x^{2}e^{x}sin(x) - 2e^{{x}*{2}}sin(x) - 11e^{{x}*{2}}cos(x) + 6e^{x} + 6xe^{x} + x^{2}e^{x} - 8e^{{x}*{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 11e^{x}sin(x)cos(x) + e^{x}cos^{2}(x) - e^{x}sin^{2}(x) + 8e^{x}sin(x) + 12xe^{x}cos(x) + 8e^{x}cos(x) + 2x^{2}e^{x}cos(x) - 2x^{2}e^{x}sin(x) - 2e^{{x}*{2}}sin(x) - 11e^{{x}*{2}}cos(x) + 6e^{x} + 6xe^{x} + x^{2}e^{x} - 8e^{{x}*{2}}\right)}{dx}\\=&11e^{x}sin(x)cos(x) + 11e^{x}cos(x)cos(x) + 11e^{x}sin(x)*-sin(x) + e^{x}cos^{2}(x) + e^{x}*-2cos(x)sin(x) - e^{x}sin^{2}(x) - e^{x}*2sin(x)cos(x) + 8e^{x}sin(x) + 8e^{x}cos(x) + 12e^{x}cos(x) + 12xe^{x}cos(x) + 12xe^{x}*-sin(x) + 8e^{x}cos(x) + 8e^{x}*-sin(x) + 2*2xe^{x}cos(x) + 2x^{2}e^{x}cos(x) + 2x^{2}e^{x}*-sin(x) - 2*2xe^{x}sin(x) - 2x^{2}e^{x}sin(x) - 2x^{2}e^{x}cos(x) - 2*2e^{x}e^{x}sin(x) - 2e^{{x}*{2}}cos(x) - 11*2e^{x}e^{x}cos(x) - 11e^{{x}*{2}}*-sin(x) + 6e^{x} + 6e^{x} + 6xe^{x} + 2xe^{x} + x^{2}e^{x} - 8*2e^{x}e^{x}\\=&7e^{x}sin(x)cos(x) + 12e^{x}cos^{2}(x) - 12e^{x}sin^{2}(x) + 28e^{x}cos(x) + 16xe^{x}cos(x) - 16xe^{x}sin(x) - 4x^{2}e^{x}sin(x) + 7e^{{x}*{2}}sin(x) - 24e^{{x}*{2}}cos(x) + 12e^{x} + 8xe^{x} + x^{2}e^{x} - 16e^{{x}*{2}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！