There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(sin(x))}^{6} + {(cos(x))}^{6}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin^{6}(x) + cos^{6}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin^{6}(x) + cos^{6}(x)\right)}{dx}\\=&6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x)\\=&6sin^{5}(x)cos(x) - 6sin(x)cos^{5}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 6sin^{5}(x)cos(x) - 6sin(x)cos^{5}(x)\right)}{dx}\\=&6*5sin^{4}(x)cos(x)cos(x) + 6sin^{5}(x)*-sin(x) - 6cos(x)cos^{5}(x) - 6sin(x)*-5cos^{4}(x)sin(x)\\=&30sin^{4}(x)cos^{2}(x) + 30sin^{2}(x)cos^{4}(x) - 6cos^{6}(x) - 6sin^{6}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 30sin^{4}(x)cos^{2}(x) + 30sin^{2}(x)cos^{4}(x) - 6cos^{6}(x) - 6sin^{6}(x)\right)}{dx}\\=&30*4sin^{3}(x)cos(x)cos^{2}(x) + 30sin^{4}(x)*-2cos(x)sin(x) + 30*2sin(x)cos(x)cos^{4}(x) + 30sin^{2}(x)*-4cos^{3}(x)sin(x) - 6*-6cos^{5}(x)sin(x) - 6*6sin^{5}(x)cos(x)\\=&-96sin^{5}(x)cos(x) + 96sin(x)cos^{5}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -96sin^{5}(x)cos(x) + 96sin(x)cos^{5}(x)\right)}{dx}\\=&-96*5sin^{4}(x)cos(x)cos(x) - 96sin^{5}(x)*-sin(x) + 96cos(x)cos^{5}(x) + 96sin(x)*-5cos^{4}(x)sin(x)\\=&-480sin^{4}(x)cos^{2}(x) - 480sin^{2}(x)cos^{4}(x) + 96cos^{6}(x) + 96sin^{6}(x)\\ \end{split}\end{equation} \]

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