There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {2}^{(x + y + 2)}{ln(2)}^{3} + y{2}^{(x + y)}{ln(2)}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {2}^{(x + y + 2)}ln^{3}(2) + y{2}^{(x + y)}ln^{4}(2)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {2}^{(x + y + 2)}ln^{3}(2) + y{2}^{(x + y)}ln^{4}(2)\right)}{dx}\\=&({2}^{(x + y + 2)}((1 + 0 + 0)ln(2) + \frac{(x + y + 2)(0)}{(2)}))ln^{3}(2) + \frac{{2}^{(x + y + 2)}*3ln^{2}(2)*0}{(2)} + y({2}^{(x + y)}((1 + 0)ln(2) + \frac{(x + y)(0)}{(2)}))ln^{4}(2) + \frac{y{2}^{(x + y)}*4ln^{3}(2)*0}{(2)}\\=&{2}^{(x + y + 2)}ln^{4}(2) + y{2}^{(x + y)}ln^{5}(2)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {2}^{(x + y + 2)}ln^{4}(2) + y{2}^{(x + y)}ln^{5}(2)\right)}{dx}\\=&({2}^{(x + y + 2)}((1 + 0 + 0)ln(2) + \frac{(x + y + 2)(0)}{(2)}))ln^{4}(2) + \frac{{2}^{(x + y + 2)}*4ln^{3}(2)*0}{(2)} + y({2}^{(x + y)}((1 + 0)ln(2) + \frac{(x + y)(0)}{(2)}))ln^{5}(2) + \frac{y{2}^{(x + y)}*5ln^{4}(2)*0}{(2)}\\=&{2}^{(x + y + 2)}ln^{5}(2) + y{2}^{(x + y)}ln^{6}(2)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {2}^{(x + y + 2)}ln^{5}(2) + y{2}^{(x + y)}ln^{6}(2)\right)}{dx}\\=&({2}^{(x + y + 2)}((1 + 0 + 0)ln(2) + \frac{(x + y + 2)(0)}{(2)}))ln^{5}(2) + \frac{{2}^{(x + y + 2)}*5ln^{4}(2)*0}{(2)} + y({2}^{(x + y)}((1 + 0)ln(2) + \frac{(x + y)(0)}{(2)}))ln^{6}(2) + \frac{y{2}^{(x + y)}*6ln^{5}(2)*0}{(2)}\\=&{2}^{(x + y + 2)}ln^{6}(2) + y{2}^{(x + y)}ln^{7}(2)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( {2}^{(x + y + 2)}ln^{6}(2) + y{2}^{(x + y)}ln^{7}(2)\right)}{dx}\\=&({2}^{(x + y + 2)}((1 + 0 + 0)ln(2) + \frac{(x + y + 2)(0)}{(2)}))ln^{6}(2) + \frac{{2}^{(x + y + 2)}*6ln^{5}(2)*0}{(2)} + y({2}^{(x + y)}((1 + 0)ln(2) + \frac{(x + y)(0)}{(2)}))ln^{7}(2) + \frac{y{2}^{(x + y)}*7ln^{6}(2)*0}{(2)}\\=&{2}^{(x + y + 2)}ln^{7}(2) + y{2}^{(x + y)}ln^{8}(2)\\ \end{split}\end{equation} \]

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