There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 8{(cos(x))}^{2} - 8{(sin(x))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 8cos^{2}(x) - 8sin^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 8cos^{2}(x) - 8sin^{2}(x)\right)}{dx}\\=&8*-2cos(x)sin(x) - 8*2sin(x)cos(x)\\=&-32sin(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -32sin(x)cos(x)\right)}{dx}\\=&-32cos(x)cos(x) - 32sin(x)*-sin(x)\\=&-32cos^{2}(x) + 32sin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -32cos^{2}(x) + 32sin^{2}(x)\right)}{dx}\\=&-32*-2cos(x)sin(x) + 32*2sin(x)cos(x)\\=&128sin(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 128sin(x)cos(x)\right)}{dx}\\=&128cos(x)cos(x) + 128sin(x)*-sin(x)\\=&128cos^{2}(x) - 128sin^{2}(x)\\ \end{split}\end{equation} \]

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