There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {y}^{(3 + 2{x}^{2})} + {x}^{y}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {y}^{(2x^{2} + 3)} + {x}^{y}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {y}^{(2x^{2} + 3)} + {x}^{y}\right)}{dx}\\=&({y}^{(2x^{2} + 3)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 3)(0)}{(y)})) + ({x}^{y}((0)ln(x) + \frac{(y)(1)}{(x)}))\\=&4x{y}^{(2x^{2} + 3)}ln(y) + \frac{y{x}^{y}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4x{y}^{(2x^{2} + 3)}ln(y) + \frac{y{x}^{y}}{x}\right)}{dx}\\=&4{y}^{(2x^{2} + 3)}ln(y) + 4x({y}^{(2x^{2} + 3)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 3)(0)}{(y)}))ln(y) + \frac{4x{y}^{(2x^{2} + 3)}*0}{(y)} + \frac{y*-{x}^{y}}{x^{2}} + \frac{y({x}^{y}((0)ln(x) + \frac{(y)(1)}{(x)}))}{x}\\=&4{y}^{(2x^{2} + 3)}ln(y) + 16x^{2}{y}^{(2x^{2} + 3)}ln^{2}(y) - \frac{y{x}^{y}}{x^{2}} + \frac{y^{2}{x}^{y}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 4{y}^{(2x^{2} + 3)}ln(y) + 16x^{2}{y}^{(2x^{2} + 3)}ln^{2}(y) - \frac{y{x}^{y}}{x^{2}} + \frac{y^{2}{x}^{y}}{x^{2}}\right)}{dx}\\=&4({y}^{(2x^{2} + 3)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 3)(0)}{(y)}))ln(y) + \frac{4{y}^{(2x^{2} + 3)}*0}{(y)} + 16*2x{y}^{(2x^{2} + 3)}ln^{2}(y) + 16x^{2}({y}^{(2x^{2} + 3)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 3)(0)}{(y)}))ln^{2}(y) + \frac{16x^{2}{y}^{(2x^{2} + 3)}*2ln(y)*0}{(y)} - \frac{y*-2{x}^{y}}{x^{3}} - \frac{y({x}^{y}((0)ln(x) + \frac{(y)(1)}{(x)}))}{x^{2}} + \frac{y^{2}*-2{x}^{y}}{x^{3}} + \frac{y^{2}({x}^{y}((0)ln(x) + \frac{(y)(1)}{(x)}))}{x^{2}}\\=&48x{y}^{(2x^{2} + 3)}ln^{2}(y) + 64x^{3}{y}^{(2x^{2} + 3)}ln^{3}(y) + \frac{2y{x}^{y}}{x^{3}} - \frac{3y^{2}{x}^{y}}{x^{3}} + \frac{y^{3}{x}^{y}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 48x{y}^{(2x^{2} + 3)}ln^{2}(y) + 64x^{3}{y}^{(2x^{2} + 3)}ln^{3}(y) + \frac{2y{x}^{y}}{x^{3}} - \frac{3y^{2}{x}^{y}}{x^{3}} + \frac{y^{3}{x}^{y}}{x^{3}}\right)}{dx}\\=&48{y}^{(2x^{2} + 3)}ln^{2}(y) + 48x({y}^{(2x^{2} + 3)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 3)(0)}{(y)}))ln^{2}(y) + \frac{48x{y}^{(2x^{2} + 3)}*2ln(y)*0}{(y)} + 64*3x^{2}{y}^{(2x^{2} + 3)}ln^{3}(y) + 64x^{3}({y}^{(2x^{2} + 3)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 3)(0)}{(y)}))ln^{3}(y) + \frac{64x^{3}{y}^{(2x^{2} + 3)}*3ln^{2}(y)*0}{(y)} + \frac{2y*-3{x}^{y}}{x^{4}} + \frac{2y({x}^{y}((0)ln(x) + \frac{(y)(1)}{(x)}))}{x^{3}} - \frac{3y^{2}*-3{x}^{y}}{x^{4}} - \frac{3y^{2}({x}^{y}((0)ln(x) + \frac{(y)(1)}{(x)}))}{x^{3}} + \frac{y^{3}*-3{x}^{y}}{x^{4}} + \frac{y^{3}({x}^{y}((0)ln(x) + \frac{(y)(1)}{(x)}))}{x^{3}}\\=&48{y}^{(2x^{2} + 3)}ln^{2}(y) + 384x^{2}{y}^{(2x^{2} + 3)}ln^{3}(y) + 256x^{4}{y}^{(2x^{2} + 3)}ln^{4}(y) - \frac{6y{x}^{y}}{x^{4}} + \frac{11y^{2}{x}^{y}}{x^{4}} - \frac{6y^{3}{x}^{y}}{x^{4}} + \frac{y^{4}{x}^{y}}{x^{4}}\\ \end{split}\end{equation} \]

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