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

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