There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (2x - 3)sin(2x + 5)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 2xsin(2x + 5) - 3sin(2x + 5)\right)}{dx}\\=&2sin(2x + 5) + 2xcos(2x + 5)(2 + 0) - 3cos(2x + 5)(2 + 0)\\=&2sin(2x + 5) + 4xcos(2x + 5) - 6cos(2x + 5)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2sin(2x + 5) + 4xcos(2x + 5) - 6cos(2x + 5)\right)}{dx}\\=&2cos(2x + 5)(2 + 0) + 4cos(2x + 5) + 4x*-sin(2x + 5)(2 + 0) - 6*-sin(2x + 5)(2 + 0)\\=&8cos(2x + 5) - 8xsin(2x + 5) + 12sin(2x + 5)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 8cos(2x + 5) - 8xsin(2x + 5) + 12sin(2x + 5)\right)}{dx}\\=&8*-sin(2x + 5)(2 + 0) - 8sin(2x + 5) - 8xcos(2x + 5)(2 + 0) + 12cos(2x + 5)(2 + 0)\\=&-24sin(2x + 5) - 16xcos(2x + 5) + 24cos(2x + 5)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -24sin(2x + 5) - 16xcos(2x + 5) + 24cos(2x + 5)\right)}{dx}\\=&-24cos(2x + 5)(2 + 0) - 16cos(2x + 5) - 16x*-sin(2x + 5)(2 + 0) + 24*-sin(2x + 5)(2 + 0)\\=&-64cos(2x + 5) + 32xsin(2x + 5) - 48sin(2x + 5)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !