There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ cos(x) + \frac{log_{7}^{x}n(sqrt(x))}{i}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos(x) + \frac{nlog_{7}^{x}sqrt(x)}{i}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos(x) + \frac{nlog_{7}^{x}sqrt(x)}{i}\right)}{dx}\\=&-sin(x) + \frac{n(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)}{i} + \frac{nlog_{7}^{x}*\frac{1}{2}}{i(x)^{\frac{1}{2}}}\\=&-sin(x) + \frac{nsqrt(x)}{ixln(7)} + \frac{nlog_{7}^{x}}{2ix^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -sin(x) + \frac{nsqrt(x)}{ixln(7)} + \frac{nlog_{7}^{x}}{2ix^{\frac{1}{2}}}\right)}{dx}\\=&-cos(x) + \frac{n*-sqrt(x)}{ix^{2}ln(7)} + \frac{n*-0sqrt(x)}{ixln^{2}(7)(7)} + \frac{n*\frac{1}{2}}{ixln(7)(x)^{\frac{1}{2}}} + \frac{n*\frac{-1}{2}log_{7}^{x}}{2ix^{\frac{3}{2}}} + \frac{n(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})}{2ix^{\frac{1}{2}}}\\=&-cos(x) - \frac{nsqrt(x)}{ix^{2}ln(7)} + \frac{n}{ix^{\frac{3}{2}}ln(7)} - \frac{nlog_{7}^{x}}{4ix^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -cos(x) - \frac{nsqrt(x)}{ix^{2}ln(7)} + \frac{n}{ix^{\frac{3}{2}}ln(7)} - \frac{nlog_{7}^{x}}{4ix^{\frac{3}{2}}}\right)}{dx}\\=&--sin(x) - \frac{n*-2sqrt(x)}{ix^{3}ln(7)} - \frac{n*-0sqrt(x)}{ix^{2}ln^{2}(7)(7)} - \frac{n*\frac{1}{2}}{ix^{2}ln(7)(x)^{\frac{1}{2}}} + \frac{n*\frac{-3}{2}}{ix^{\frac{5}{2}}ln(7)} + \frac{n*-0}{ix^{\frac{3}{2}}ln^{2}(7)(7)} - \frac{n*\frac{-3}{2}log_{7}^{x}}{4ix^{\frac{5}{2}}} - \frac{n(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})}{4ix^{\frac{3}{2}}}\\=&sin(x) + \frac{2nsqrt(x)}{ix^{3}ln(7)} - \frac{9n}{4ix^{\frac{5}{2}}ln(7)} + \frac{3nlog_{7}^{x}}{8ix^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( sin(x) + \frac{2nsqrt(x)}{ix^{3}ln(7)} - \frac{9n}{4ix^{\frac{5}{2}}ln(7)} + \frac{3nlog_{7}^{x}}{8ix^{\frac{5}{2}}}\right)}{dx}\\=&cos(x) + \frac{2n*-3sqrt(x)}{ix^{4}ln(7)} + \frac{2n*-0sqrt(x)}{ix^{3}ln^{2}(7)(7)} + \frac{2n*\frac{1}{2}}{ix^{3}ln(7)(x)^{\frac{1}{2}}} - \frac{9n*\frac{-5}{2}}{4ix^{\frac{7}{2}}ln(7)} - \frac{9n*-0}{4ix^{\frac{5}{2}}ln^{2}(7)(7)} + \frac{3n*\frac{-5}{2}log_{7}^{x}}{8ix^{\frac{7}{2}}} + \frac{3n(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})}{8ix^{\frac{5}{2}}}\\=&cos(x) - \frac{6nsqrt(x)}{ix^{4}ln(7)} + \frac{7n}{ix^{\frac{7}{2}}ln(7)} - \frac{15nlog_{7}^{x}}{16ix^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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