There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 4{x}^{4} + 3{{x}^{2}}^{y}*3 - 2{x}^{2}{y}^{4} + xy + 5\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4x^{4} + 9{x^{2}}^{y} - 2y^{4}x^{2} + yx + 5\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4x^{4} + 9{x^{2}}^{y} - 2y^{4}x^{2} + yx + 5\right)}{dx}\\=&4*4x^{3} + 9({x^{2}}^{y}((0)ln(x^{2}) + \frac{(y)(2x)}{(x^{2})})) - 2y^{4}*2x + y + 0\\=&16x^{3} + \frac{18y{x^{2}}^{y}}{x} - 4y^{4}x + y\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 16x^{3} + \frac{18y{x^{2}}^{y}}{x} - 4y^{4}x + y\right)}{dx}\\=&16*3x^{2} + \frac{18y*-{x^{2}}^{y}}{x^{2}} + \frac{18y({x^{2}}^{y}((0)ln(x^{2}) + \frac{(y)(2x)}{(x^{2})}))}{x} - 4y^{4} + 0\\=&48x^{2} - \frac{18y{x^{2}}^{y}}{x^{2}} + \frac{36y^{2}{x^{2}}^{y}}{x^{2}} - 4y^{4}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 48x^{2} - \frac{18y{x^{2}}^{y}}{x^{2}} + \frac{36y^{2}{x^{2}}^{y}}{x^{2}} - 4y^{4}\right)}{dx}\\=&48*2x - \frac{18y*-2{x^{2}}^{y}}{x^{3}} - \frac{18y({x^{2}}^{y}((0)ln(x^{2}) + \frac{(y)(2x)}{(x^{2})}))}{x^{2}} + \frac{36y^{2}*-2{x^{2}}^{y}}{x^{3}} + \frac{36y^{2}({x^{2}}^{y}((0)ln(x^{2}) + \frac{(y)(2x)}{(x^{2})}))}{x^{2}} + 0\\=&96x + \frac{36y{x^{2}}^{y}}{x^{3}} - \frac{108y^{2}{x^{2}}^{y}}{x^{3}} + \frac{72y^{3}{x^{2}}^{y}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 96x + \frac{36y{x^{2}}^{y}}{x^{3}} - \frac{108y^{2}{x^{2}}^{y}}{x^{3}} + \frac{72y^{3}{x^{2}}^{y}}{x^{3}}\right)}{dx}\\=&96 + \frac{36y*-3{x^{2}}^{y}}{x^{4}} + \frac{36y({x^{2}}^{y}((0)ln(x^{2}) + \frac{(y)(2x)}{(x^{2})}))}{x^{3}} - \frac{108y^{2}*-3{x^{2}}^{y}}{x^{4}} - \frac{108y^{2}({x^{2}}^{y}((0)ln(x^{2}) + \frac{(y)(2x)}{(x^{2})}))}{x^{3}} + \frac{72y^{3}*-3{x^{2}}^{y}}{x^{4}} + \frac{72y^{3}({x^{2}}^{y}((0)ln(x^{2}) + \frac{(y)(2x)}{(x^{2})}))}{x^{3}}\\=& - \frac{108y{x^{2}}^{y}}{x^{4}} + \frac{396y^{2}{x^{2}}^{y}}{x^{4}} - \frac{432y^{3}{x^{2}}^{y}}{x^{4}} + \frac{144y^{4}{x^{2}}^{y}}{x^{4}} + 96\\ \end{split}\end{equation} \]

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