There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(x + 1)}^{(x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x + 1)^{(x + 1)}\right)}{dx}\\=&((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))\\=&(x + 1)^{(x + 1)}ln(x + 1) + (x + 1)^{(x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( (x + 1)^{(x + 1)}ln(x + 1) + (x + 1)^{(x + 1)}\right)}{dx}\\=&((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))ln(x + 1) + \frac{(x + 1)^{(x + 1)}(1 + 0)}{(x + 1)} + ((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))\\=&(x + 1)^{(x + 1)}ln^{2}(x + 1) + 2(x + 1)^{(x + 1)}ln(x + 1) + \frac{(x + 1)^{(x + 1)}}{(x + 1)} + (x + 1)^{(x + 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( (x + 1)^{(x + 1)}ln^{2}(x + 1) + 2(x + 1)^{(x + 1)}ln(x + 1) + \frac{(x + 1)^{(x + 1)}}{(x + 1)} + (x + 1)^{(x + 1)}\right)}{dx}\\=&((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))ln^{2}(x + 1) + \frac{(x + 1)^{(x + 1)}*2ln(x + 1)(1 + 0)}{(x + 1)} + 2((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))ln(x + 1) + \frac{2(x + 1)^{(x + 1)}(1 + 0)}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}})(x + 1)^{(x + 1)} + \frac{((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))}{(x + 1)} + ((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))\\=&(x + 1)^{(x + 1)}ln^{3}(x + 1) + 3(x + 1)^{(x + 1)}ln^{2}(x + 1) + \frac{3(x + 1)^{(x + 1)}ln(x + 1)}{(x + 1)} + 3(x + 1)^{(x + 1)}ln(x + 1) + \frac{3(x + 1)^{(x + 1)}}{(x + 1)} - \frac{(x + 1)^{(x + 1)}}{(x + 1)^{2}} + (x + 1)^{(x + 1)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( (x + 1)^{(x + 1)}ln^{3}(x + 1) + 3(x + 1)^{(x + 1)}ln^{2}(x + 1) + \frac{3(x + 1)^{(x + 1)}ln(x + 1)}{(x + 1)} + 3(x + 1)^{(x + 1)}ln(x + 1) + \frac{3(x + 1)^{(x + 1)}}{(x + 1)} - \frac{(x + 1)^{(x + 1)}}{(x + 1)^{2}} + (x + 1)^{(x + 1)}\right)}{dx}\\=&((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))ln^{3}(x + 1) + \frac{(x + 1)^{(x + 1)}*3ln^{2}(x + 1)(1 + 0)}{(x + 1)} + 3((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))ln^{2}(x + 1) + \frac{3(x + 1)^{(x + 1)}*2ln(x + 1)(1 + 0)}{(x + 1)} + 3(\frac{-(1 + 0)}{(x + 1)^{2}})(x + 1)^{(x + 1)}ln(x + 1) + \frac{3((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))ln(x + 1)}{(x + 1)} + \frac{3(x + 1)^{(x + 1)}(1 + 0)}{(x + 1)(x + 1)} + 3((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))ln(x + 1) + \frac{3(x + 1)^{(x + 1)}(1 + 0)}{(x + 1)} + 3(\frac{-(1 + 0)}{(x + 1)^{2}})(x + 1)^{(x + 1)} + \frac{3((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))}{(x + 1)} - (\frac{-2(1 + 0)}{(x + 1)^{3}})(x + 1)^{(x + 1)} - \frac{((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))}{(x + 1)^{2}} + ((x + 1)^{(x + 1)}((1 + 0)ln(x + 1) + \frac{(x + 1)(1 + 0)}{(x + 1)}))\\=&(x + 1)^{(x + 1)}ln^{4}(x + 1) + 4(x + 1)^{(x + 1)}ln^{3}(x + 1) + \frac{6(x + 1)^{(x + 1)}ln^{2}(x + 1)}{(x + 1)} + 6(x + 1)^{(x + 1)}ln^{2}(x + 1) + \frac{12(x + 1)^{(x + 1)}ln(x + 1)}{(x + 1)} - \frac{4(x + 1)^{(x + 1)}ln(x + 1)}{(x + 1)^{2}} + 4(x + 1)^{(x + 1)}ln(x + 1) + \frac{6(x + 1)^{(x + 1)}}{(x + 1)} + \frac{2(x + 1)^{(x + 1)}}{(x + 1)^{3}} - \frac{(x + 1)^{(x + 1)}}{(x + 1)^{2}} + (x + 1)^{(x + 1)}\\ \end{split}\end{equation} \]

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