There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 9e^{16x} + 18e^{8x} + 54e^{4x} + 216e^{2x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 9e^{16x} + 18e^{8x} + 54e^{4x} + 216e^{2x}\right)}{dx}\\=&9e^{16x}*16 + 18e^{8x}*8 + 54e^{4x}*4 + 216e^{2x}*2\\=&144e^{16x} + 144e^{8x} + 216e^{4x} + 432e^{2x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 144e^{16x} + 144e^{8x} + 216e^{4x} + 432e^{2x}\right)}{dx}\\=&144e^{16x}*16 + 144e^{8x}*8 + 216e^{4x}*4 + 432e^{2x}*2\\=&2304e^{16x} + 1152e^{8x} + 864e^{4x} + 864e^{2x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2304e^{16x} + 1152e^{8x} + 864e^{4x} + 864e^{2x}\right)}{dx}\\=&2304e^{16x}*16 + 1152e^{8x}*8 + 864e^{4x}*4 + 864e^{2x}*2\\=&36864e^{16x} + 9216e^{8x} + 3456e^{4x} + 1728e^{2x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 36864e^{16x} + 9216e^{8x} + 3456e^{4x} + 1728e^{2x}\right)}{dx}\\=&36864e^{16x}*16 + 9216e^{8x}*8 + 3456e^{4x}*4 + 1728e^{2x}*2\\=&589824e^{16x} + 73728e^{8x} + 13824e^{4x} + 3456e^{2x}\\ \end{split}\end{equation} \]

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