There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ tan(45x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan(45x)\right)}{dx}\\=&sec^{2}(45x)(45)\\=&45sec^{2}(45x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 45sec^{2}(45x)\right)}{dx}\\=&45*2sec^{2}(45x)tan(45x)*45\\=&4050tan(45x)sec^{2}(45x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 4050tan(45x)sec^{2}(45x)\right)}{dx}\\=&4050sec^{2}(45x)(45)sec^{2}(45x) + 4050tan(45x)*2sec^{2}(45x)tan(45x)*45\\=&182250sec^{4}(45x) + 364500tan^{2}(45x)sec^{2}(45x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 182250sec^{4}(45x) + 364500tan^{2}(45x)sec^{2}(45x)\right)}{dx}\\=&182250*4sec^{4}(45x)tan(45x)*45 + 364500*2tan(45x)sec^{2}(45x)(45)sec^{2}(45x) + 364500tan^{2}(45x)*2sec^{2}(45x)tan(45x)*45\\=&65610000tan(45x)sec^{4}(45x) + 32805000tan^{3}(45x)sec^{2}(45x)\\ \end{split}\end{equation} \]

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