There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin({({x}^{2})}^{{x}^{2}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin({x^{2}}^{x^{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin({x^{2}}^{x^{2}})\right)}{dx}\\=&cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})\right)}{dx}\\=&2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{2x{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 2x{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 2{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 2x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}})\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}})\right)}{dx}\\=&2({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{2{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 2{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 4*2x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4x^{2}{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{8x^{2}{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 6({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 4*2x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 4x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{4x^{2}{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*2x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{8x^{2}{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 4*2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 4x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 4*2x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 4x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&12x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}})\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}})\right)}{dx}\\=&12{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 12x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{12x{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 12x{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 48{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 48x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{48x{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 48x{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + \frac{4*-{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x^{2}} + \frac{4({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}})}{x} + \frac{4{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))}{x} - 12{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 12x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{12x{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 48{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 48x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{48x{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 48x{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*3x^{2}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{8x^{3}{x^{2}}^{x^{2}}*3ln^{2}(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 24*3x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{24x^{3}{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(2x^{2})}*3ln^{2}(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 72*3x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{72x^{3}{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 24*3x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{24x^{3}{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 36{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 36x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 72*3x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{72x^{3}{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 36{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 36x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*3x^{2}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 8x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - \frac{8x^{3}{x^{2}}^{(3x^{2})}*3ln^{2}(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(3x^{2})}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(3x^{2})}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*3x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 8x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*3x^{2}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) - 8x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&12{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x^{2}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 240x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 104{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) - 144x^{2}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 720x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 336x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 140{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 1008x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x^{2}} - 104{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 140{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 12{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x^{2}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 240x^{2}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 336x^{2}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{x^{2}}ln^{4}(x^{2})cos({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 112x^{4}{x^{2}}^{(2x^{2})}ln^{4}(x^{2})sin({x^{2}}^{x^{2}}) - 448x^{4}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) + 96x^{4}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 672x^{4}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 96x^{4}{x^{2}}^{(3x^{2})}ln^{4}(x^{2})cos({x^{2}}^{x^{2}}) - 384x^{4}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 576x^{4}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 144x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 448x^{4}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 432x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 384x^{4}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) - 144x^{2}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{(4x^{2})}ln^{4}(x^{2})sin({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{(4x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) + 96x^{4}{x^{2}}^{(4x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{(4x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 112x^{4}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 96x^{4}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{(4x^{2})}sin({x^{2}}^{x^{2}})\\ \end{split}\end{equation} \]

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