There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 12345sin(x)cos(x)tan(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 12345sin(x)cos(x)tan(x)\right)}{dx}\\=&12345cos(x)cos(x)tan(x) + 12345sin(x)*-sin(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)(1)\\=&12345cos^{2}(x)tan(x) - 12345sin^{2}(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 12345cos^{2}(x)tan(x) - 12345sin^{2}(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)\right)}{dx}\\=&12345*-2cos(x)sin(x)tan(x) + 12345cos^{2}(x)sec^{2}(x)(1) - 12345*2sin(x)cos(x)tan(x) - 12345sin^{2}(x)sec^{2}(x)(1) + 12345cos(x)cos(x)sec^{2}(x) + 12345sin(x)*-sin(x)sec^{2}(x) + 12345sin(x)cos(x)*2sec^{2}(x)tan(x)\\=&24690sin(x)cos(x)tan(x)sec^{2}(x) + 24690cos^{2}(x)sec^{2}(x) - 49380sin(x)cos(x)tan(x) - 24690sin^{2}(x)sec^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 24690sin(x)cos(x)tan(x)sec^{2}(x) + 24690cos^{2}(x)sec^{2}(x) - 49380sin(x)cos(x)tan(x) - 24690sin^{2}(x)sec^{2}(x)\right)}{dx}\\=&24690cos(x)cos(x)tan(x)sec^{2}(x) + 24690sin(x)*-sin(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) + 24690sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) + 24690*-2cos(x)sin(x)sec^{2}(x) + 24690cos^{2}(x)*2sec^{2}(x)tan(x) - 49380cos(x)cos(x)tan(x) - 49380sin(x)*-sin(x)tan(x) - 49380sin(x)cos(x)sec^{2}(x)(1) - 24690*2sin(x)cos(x)sec^{2}(x) - 24690sin^{2}(x)*2sec^{2}(x)tan(x)\\=&74070cos^{2}(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{4}(x) + 49380sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140sin(x)cos(x)sec^{2}(x) - 49380cos^{2}(x)tan(x) + 49380sin^{2}(x)tan(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 74070cos^{2}(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{4}(x) + 49380sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140sin(x)cos(x)sec^{2}(x) - 49380cos^{2}(x)tan(x) + 49380sin^{2}(x)tan(x)\right)}{dx}\\=&74070*-2cos(x)sin(x)tan(x)sec^{2}(x) + 74070cos^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 74070cos^{2}(x)tan(x)*2sec^{2}(x)tan(x) - 74070*2sin(x)cos(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 74070sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) + 24690cos(x)cos(x)sec^{4}(x) + 24690sin(x)*-sin(x)sec^{4}(x) + 24690sin(x)cos(x)*4sec^{4}(x)tan(x) + 49380cos(x)cos(x)tan^{2}(x)sec^{2}(x) + 49380sin(x)*-sin(x)tan^{2}(x)sec^{2}(x) + 49380sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 49380sin(x)cos(x)tan^{2}(x)*2sec^{2}(x)tan(x) - 148140cos(x)cos(x)sec^{2}(x) - 148140sin(x)*-sin(x)sec^{2}(x) - 148140sin(x)cos(x)*2sec^{2}(x)tan(x) - 49380*-2cos(x)sin(x)tan(x) - 49380cos^{2}(x)sec^{2}(x)(1) + 49380*2sin(x)cos(x)tan(x) + 49380sin^{2}(x)sec^{2}(x)(1)\\=&197520sin(x)cos(x)tan(x)sec^{4}(x) + 98760cos^{2}(x)sec^{4}(x) + 197520cos^{2}(x)tan^{2}(x)sec^{2}(x) - 592560sin(x)cos(x)tan(x)sec^{2}(x) - 98760sin^{2}(x)sec^{4}(x) - 197520sin^{2}(x)tan^{2}(x)sec^{2}(x) + 98760sin(x)cos(x)tan^{3}(x)sec^{2}(x) - 197520cos^{2}(x)sec^{2}(x) + 197520sin^{2}(x)sec^{2}(x) + 197520sin(x)cos(x)tan(x)\\ \end{split}\end{equation} \]

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