There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(x + 1)}^{a}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x + 1)^{a}\right)}{dx}\\=&((x + 1)^{a}((0)ln(x + 1) + \frac{(a)(1 + 0)}{(x + 1)}))\\=&\frac{a(x + 1)^{a}}{(x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{a(x + 1)^{a}}{(x + 1)}\right)}{dx}\\=&(\frac{-(1 + 0)}{(x + 1)^{2}})a(x + 1)^{a} + \frac{a((x + 1)^{a}((0)ln(x + 1) + \frac{(a)(1 + 0)}{(x + 1)}))}{(x + 1)}\\=&\frac{-a(x + 1)^{a}}{(x + 1)^{2}} + \frac{a^{2}(x + 1)^{a}}{(x + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-a(x + 1)^{a}}{(x + 1)^{2}} + \frac{a^{2}(x + 1)^{a}}{(x + 1)^{2}}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x + 1)^{3}})a(x + 1)^{a} - \frac{a((x + 1)^{a}((0)ln(x + 1) + \frac{(a)(1 + 0)}{(x + 1)}))}{(x + 1)^{2}} + (\frac{-2(1 + 0)}{(x + 1)^{3}})a^{2}(x + 1)^{a} + \frac{a^{2}((x + 1)^{a}((0)ln(x + 1) + \frac{(a)(1 + 0)}{(x + 1)}))}{(x + 1)^{2}}\\=&\frac{2a(x + 1)^{a}}{(x + 1)^{3}} - \frac{3a^{2}(x + 1)^{a}}{(x + 1)^{3}} + \frac{a^{3}(x + 1)^{a}}{(x + 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2a(x + 1)^{a}}{(x + 1)^{3}} - \frac{3a^{2}(x + 1)^{a}}{(x + 1)^{3}} + \frac{a^{3}(x + 1)^{a}}{(x + 1)^{3}}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x + 1)^{4}})a(x + 1)^{a} + \frac{2a((x + 1)^{a}((0)ln(x + 1) + \frac{(a)(1 + 0)}{(x + 1)}))}{(x + 1)^{3}} - 3(\frac{-3(1 + 0)}{(x + 1)^{4}})a^{2}(x + 1)^{a} - \frac{3a^{2}((x + 1)^{a}((0)ln(x + 1) + \frac{(a)(1 + 0)}{(x + 1)}))}{(x + 1)^{3}} + (\frac{-3(1 + 0)}{(x + 1)^{4}})a^{3}(x + 1)^{a} + \frac{a^{3}((x + 1)^{a}((0)ln(x + 1) + \frac{(a)(1 + 0)}{(x + 1)}))}{(x + 1)^{3}}\\=&\frac{-6a(x + 1)^{a}}{(x + 1)^{4}} + \frac{11a^{2}(x + 1)^{a}}{(x + 1)^{4}} - \frac{6a^{3}(x + 1)^{a}}{(x + 1)^{4}} + \frac{a^{4}(x + 1)^{a}}{(x + 1)^{4}}\\ \end{split}\end{equation} \]

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