There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ xsin(x) - e^{{x}^{2}} + 1\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = xsin(x) - e^{x^{2}} + 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xsin(x) - e^{x^{2}} + 1\right)}{dx}\\=&sin(x) + xcos(x) - e^{x^{2}}*2x + 0\\=&sin(x) + xcos(x) - 2xe^{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sin(x) + xcos(x) - 2xe^{x^{2}}\right)}{dx}\\=&cos(x) + cos(x) + x*-sin(x) - 2e^{x^{2}} - 2xe^{x^{2}}*2x\\=&2cos(x) - xsin(x) - 2e^{x^{2}} - 4x^{2}e^{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2cos(x) - xsin(x) - 2e^{x^{2}} - 4x^{2}e^{x^{2}}\right)}{dx}\\=&2*-sin(x) - sin(x) - xcos(x) - 2e^{x^{2}}*2x - 4*2xe^{x^{2}} - 4x^{2}e^{x^{2}}*2x\\=&-3sin(x) - xcos(x) - 12xe^{x^{2}} - 8x^{3}e^{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -3sin(x) - xcos(x) - 12xe^{x^{2}} - 8x^{3}e^{x^{2}}\right)}{dx}\\=&-3cos(x) - cos(x) - x*-sin(x) - 12e^{x^{2}} - 12xe^{x^{2}}*2x - 8*3x^{2}e^{x^{2}} - 8x^{3}e^{x^{2}}*2x\\=&-4cos(x) + xsin(x) - 12e^{x^{2}} - 48x^{2}e^{x^{2}} - 16x^{4}e^{x^{2}}\\ \end{split}\end{equation} \]

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