There are 1 questions in this calculation: for each question, the 4 derivative of y is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 4{x}^{4} + 3{x}^{2}{y}^{3} - 2{x}^{2}{y}^{4} + xy + 5\ with\ respect\ to\ y：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3x^{2}y^{3} - 2x^{2}y^{4} + xy + 4x^{4} + 5\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3x^{2}y^{3} - 2x^{2}y^{4} + xy + 4x^{4} + 5\right)}{dy}\\=&3x^{2}*3y^{2} - 2x^{2}*4y^{3} + x + 0 + 0\\=&9x^{2}y^{2} - 8x^{2}y^{3} + x\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 9x^{2}y^{2} - 8x^{2}y^{3} + x\right)}{dy}\\=&9x^{2}*2y - 8x^{2}*3y^{2} + 0\\=&18x^{2}y - 24x^{2}y^{2}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 18x^{2}y - 24x^{2}y^{2}\right)}{dy}\\=&18x^{2} - 24x^{2}*2y\\=& - 48x^{2}y + 18x^{2}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 48x^{2}y + 18x^{2}\right)}{dy}\\=& - 48x^{2} + 0\\=& - 48x^{2}\\ \end{split}\end{equation} \]

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