There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{{3}^{x}}(ln({e}^{2022}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2022e^{{3}^{x}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2022e^{{3}^{x}}\right)}{dx}\\=&2022e^{{3}^{x}}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))\\=&2022 * {3}^{x}e^{{3}^{x}}ln(3)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2022 * {3}^{x}e^{{3}^{x}}ln(3)\right)}{dx}\\=&2022({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))e^{{3}^{x}}ln(3) + 2022 * {3}^{x}e^{{3}^{x}}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln(3) + \frac{2022 * {3}^{x}e^{{3}^{x}}*0}{(3)}\\=&2022 * {3}^{x}e^{{3}^{x}}ln^{2}(3) + 2022 * {3}^{(2x)}e^{{3}^{x}}ln^{2}(3)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2022 * {3}^{x}e^{{3}^{x}}ln^{2}(3) + 2022 * {3}^{(2x)}e^{{3}^{x}}ln^{2}(3)\right)}{dx}\\=&2022({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))e^{{3}^{x}}ln^{2}(3) + 2022 * {3}^{x}e^{{3}^{x}}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{2}(3) + \frac{2022 * {3}^{x}e^{{3}^{x}}*2ln(3)*0}{(3)} + 2022({3}^{(2x)}((2)ln(3) + \frac{(2x)(0)}{(3)}))e^{{3}^{x}}ln^{2}(3) + 2022 * {3}^{(2x)}e^{{3}^{x}}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{2}(3) + \frac{2022 * {3}^{(2x)}e^{{3}^{x}}*2ln(3)*0}{(3)}\\=&2022 * {3}^{x}e^{{3}^{x}}ln^{3}(3) + 6066 * {3}^{(2x)}e^{{3}^{x}}ln^{3}(3) + 2022 * {3}^{(3x)}e^{{3}^{x}}ln^{3}(3)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 2022 * {3}^{x}e^{{3}^{x}}ln^{3}(3) + 6066 * {3}^{(2x)}e^{{3}^{x}}ln^{3}(3) + 2022 * {3}^{(3x)}e^{{3}^{x}}ln^{3}(3)\right)}{dx}\\=&2022({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))e^{{3}^{x}}ln^{3}(3) + 2022 * {3}^{x}e^{{3}^{x}}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{3}(3) + \frac{2022 * {3}^{x}e^{{3}^{x}}*3ln^{2}(3)*0}{(3)} + 6066({3}^{(2x)}((2)ln(3) + \frac{(2x)(0)}{(3)}))e^{{3}^{x}}ln^{3}(3) + 6066 * {3}^{(2x)}e^{{3}^{x}}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{3}(3) + \frac{6066 * {3}^{(2x)}e^{{3}^{x}}*3ln^{2}(3)*0}{(3)} + 2022({3}^{(3x)}((3)ln(3) + \frac{(3x)(0)}{(3)}))e^{{3}^{x}}ln^{3}(3) + 2022 * {3}^{(3x)}e^{{3}^{x}}({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))ln^{3}(3) + \frac{2022 * {3}^{(3x)}e^{{3}^{x}}*3ln^{2}(3)*0}{(3)}\\=&2022 * {3}^{x}e^{{3}^{x}}ln^{4}(3) + 14154 * {3}^{(2x)}e^{{3}^{x}}ln^{4}(3) + 12132 * {3}^{(3x)}e^{{3}^{x}}ln^{4}(3) + 2022 * {3}^{(4x)}e^{{3}^{x}}ln^{4}(3)\\ \end{split}\end{equation} \]

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