There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {2}^{lg(sin(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {2}^{lg(sin(x))}\right)}{dx}\\=&({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))\\=&\frac{{2}^{lg(sin(x))}ln(2)cos(x)}{ln{10}sin(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{2}^{lg(sin(x))}ln(2)cos(x)}{ln{10}sin(x)}\right)}{dx}\\=&\frac{({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln(2)cos(x)}{ln{10}sin(x)} + \frac{{2}^{lg(sin(x))}*0cos(x)}{(2)ln{10}sin(x)} + \frac{{2}^{lg(sin(x))}ln(2)*-0cos(x)}{ln^{2}{10}sin(x)} + \frac{{2}^{lg(sin(x))}ln(2)*-cos(x)cos(x)}{ln{10}sin^{2}(x)} + \frac{{2}^{lg(sin(x))}ln(2)*-sin(x)}{ln{10}sin(x)}\\=&\frac{{2}^{lg(sin(x))}ln^{2}(2)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{2}^{lg(sin(x))}ln(2)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{2}^{lg(sin(x))}ln(2)}{ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{{2}^{lg(sin(x))}ln^{2}(2)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{2}^{lg(sin(x))}ln(2)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{2}^{lg(sin(x))}ln(2)}{ln{10}}\right)}{dx}\\=&\frac{({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln^{2}(2)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} + \frac{{2}^{lg(sin(x))}*2ln(2)*0cos^{2}(x)}{(2)ln^{2}{10}sin^{2}(x)} + \frac{{2}^{lg(sin(x))}ln^{2}(2)*-2*0cos^{2}(x)}{ln^{3}{10}sin^{2}(x)} + \frac{{2}^{lg(sin(x))}ln^{2}(2)*-2cos(x)cos^{2}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{{2}^{lg(sin(x))}ln^{2}(2)*-2cos(x)sin(x)}{ln^{2}{10}sin^{2}(x)} - \frac{({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln(2)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{2}^{lg(sin(x))}*0cos^{2}(x)}{(2)ln{10}sin^{2}(x)} - \frac{{2}^{lg(sin(x))}ln(2)*-0cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{2}^{lg(sin(x))}ln(2)*-2cos(x)cos^{2}(x)}{ln{10}sin^{3}(x)} - \frac{{2}^{lg(sin(x))}ln(2)*-2cos(x)sin(x)}{ln{10}sin^{2}(x)} - \frac{({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln(2)}{ln{10}} - \frac{{2}^{lg(sin(x))}*0}{(2)ln{10}} - \frac{{2}^{lg(sin(x))}ln(2)*-0}{ln^{2}{10}}\\=&\frac{{2}^{lg(sin(x))}ln^{3}(2)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)cos^{3}(x)}{ln{10}sin^{3}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)cos(x)}{ln{10}sin(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{{2}^{lg(sin(x))}ln^{3}(2)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)cos^{3}(x)}{ln{10}sin^{3}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)cos(x)}{ln{10}sin(x)}\right)}{dx}\\=&\frac{({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln^{3}(2)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} + \frac{{2}^{lg(sin(x))}*3ln^{2}(2)*0cos^{3}(x)}{(2)ln^{3}{10}sin^{3}(x)} + \frac{{2}^{lg(sin(x))}ln^{3}(2)*-3*0cos^{3}(x)}{ln^{4}{10}sin^{3}(x)} + \frac{{2}^{lg(sin(x))}ln^{3}(2)*-3cos(x)cos^{3}(x)}{ln^{3}{10}sin^{4}(x)} + \frac{{2}^{lg(sin(x))}ln^{3}(2)*-3cos^{2}(x)sin(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln^{2}(2)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} - \frac{3 * {2}^{lg(sin(x))}*2ln(2)*0cos^{3}(x)}{(2)ln^{2}{10}sin^{3}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)*-2*0cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)*-3cos(x)cos^{3}(x)}{ln^{2}{10}sin^{4}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)*-3cos^{2}(x)sin(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln(2)cos^{3}(x)}{ln{10}sin^{3}(x)} + \frac{2 * {2}^{lg(sin(x))}*0cos^{3}(x)}{(2)ln{10}sin^{3}(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)*-0cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)*-3cos(x)cos^{3}(x)}{ln{10}sin^{4}(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)*-3cos^{2}(x)sin(x)}{ln{10}sin^{3}(x)} - \frac{3({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln^{2}(2)cos(x)}{ln^{2}{10}sin(x)} - \frac{3 * {2}^{lg(sin(x))}*2ln(2)*0cos(x)}{(2)ln^{2}{10}sin(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)*-2*0cos(x)}{ln^{3}{10}sin(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)*-cos(x)cos(x)}{ln^{2}{10}sin^{2}(x)} - \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)*-sin(x)}{ln^{2}{10}sin(x)} + \frac{2({2}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(2) + \frac{(lg(sin(x)))(0)}{(2)}))ln(2)cos(x)}{ln{10}sin(x)} + \frac{2 * {2}^{lg(sin(x))}*0cos(x)}{(2)ln{10}sin(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)*-0cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)*-cos(x)cos(x)}{ln{10}sin^{2}(x)} + \frac{2 * {2}^{lg(sin(x))}ln(2)*-sin(x)}{ln{10}sin(x)}\\=&\frac{{2}^{lg(sin(x))}ln^{4}(2)cos^{4}(x)}{ln^{4}{10}sin^{4}(x)} - \frac{6 * {2}^{lg(sin(x))}ln^{3}(2)cos^{4}(x)}{ln^{3}{10}sin^{4}(x)} + \frac{11 * {2}^{lg(sin(x))}ln^{2}(2)cos^{4}(x)}{ln^{2}{10}sin^{4}(x)} - \frac{6 * {2}^{lg(sin(x))}ln^{3}(2)cos^{2}(x)}{ln^{3}{10}sin^{2}(x)} - \frac{6 * {2}^{lg(sin(x))}ln(2)cos^{4}(x)}{ln{10}sin^{4}(x)} + \frac{14 * {2}^{lg(sin(x))}ln^{2}(2)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{8 * {2}^{lg(sin(x))}ln(2)cos^{2}(x)}{ln{10}sin^{2}(x)} + \frac{3 * {2}^{lg(sin(x))}ln^{2}(2)}{ln^{2}{10}} - \frac{2 * {2}^{lg(sin(x))}ln(2)}{ln{10}}\\ \end{split}\end{equation} \]Your problem has not been solved here? 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