There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ (tan(x))tan(x) - {x}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = tan^{2}(x) - x^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan^{2}(x) - x^{2}\right)}{dx}\\=&2tan(x)sec^{2}(x)(1) - 2x\\=&2tan(x)sec^{2}(x) - 2x\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2tan(x)sec^{2}(x) - 2x\right)}{dx}\\=&2sec^{2}(x)(1)sec^{2}(x) + 2tan(x)*2sec^{2}(x)tan(x) - 2\\=&2sec^{4}(x) + 4tan^{2}(x)sec^{2}(x) - 2\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2sec^{4}(x) + 4tan^{2}(x)sec^{2}(x) - 2\right)}{dx}\\=&2*4sec^{4}(x)tan(x) + 4*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4tan^{2}(x)*2sec^{2}(x)tan(x) + 0\\=&16tan(x)sec^{4}(x) + 8tan^{3}(x)sec^{2}(x)\\ \end{split}\end{equation} \]

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