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

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