There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {x}^{4} + {x}^{3} + {sin(x)}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{4} + x^{3} + sin^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{4} + x^{3} + sin^{2}(x)\right)}{dx}\\=&4x^{3} + 3x^{2} + 2sin(x)cos(x)\\=&4x^{3} + 3x^{2} + 2sin(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4x^{3} + 3x^{2} + 2sin(x)cos(x)\right)}{dx}\\=&4*3x^{2} + 3*2x + 2cos(x)cos(x) + 2sin(x)*-sin(x)\\=&12x^{2} + 6x + 2cos^{2}(x) - 2sin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12x^{2} + 6x + 2cos^{2}(x) - 2sin^{2}(x)\right)}{dx}\\=&12*2x + 6 + 2*-2cos(x)sin(x) - 2*2sin(x)cos(x)\\=&24x - 8sin(x)cos(x) + 6\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24x - 8sin(x)cos(x) + 6\right)}{dx}\\=&24 - 8cos(x)cos(x) - 8sin(x)*-sin(x) + 0\\=& - 8cos^{2}(x) + 8sin^{2}(x) + 24\\ \end{split}\end{equation} \]

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