There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{1}{(2{(x + 1)}^{\frac{1}{2}})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{2}}{(x + 1)^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{2}}{(x + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{1}{2}(\frac{\frac{-1}{2}(1 + 0)}{(x + 1)^{\frac{3}{2}}})\\=&\frac{-1}{4(x + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{4(x + 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-(\frac{\frac{-3}{2}(1 + 0)}{(x + 1)^{\frac{5}{2}}})}{4}\\=&\frac{3}{8(x + 1)^{\frac{5}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{3}{8(x + 1)^{\frac{5}{2}}}\right)}{dx}\\=&\frac{3(\frac{\frac{-5}{2}(1 + 0)}{(x + 1)^{\frac{7}{2}}})}{8}\\=&\frac{-15}{16(x + 1)^{\frac{7}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-15}{16(x + 1)^{\frac{7}{2}}}\right)}{dx}\\=&\frac{-15(\frac{\frac{-7}{2}(1 + 0)}{(x + 1)^{\frac{9}{2}}})}{16}\\=&\frac{105}{32(x + 1)^{\frac{9}{2}}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！