There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ e^{sin(pix)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{sin(pix)}\right)}{dx}\\=&e^{sin(pix)}cos(pix)pi\\=&pie^{sin(pix)}cos(pix)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( pie^{sin(pix)}cos(pix)\right)}{dx}\\=&pie^{sin(pix)}cos(pix)picos(pix) + pie^{sin(pix)}*-sin(pix)pi\\=&p^{2}i^{2}e^{sin(pix)}cos^{2}(pix) - p^{2}i^{2}e^{sin(pix)}sin(pix)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( p^{2}i^{2}e^{sin(pix)}cos^{2}(pix) - p^{2}i^{2}e^{sin(pix)}sin(pix)\right)}{dx}\\=&p^{2}i^{2}e^{sin(pix)}cos(pix)picos^{2}(pix) + p^{2}i^{2}e^{sin(pix)}*-2cos(pix)sin(pix)pi - p^{2}i^{2}e^{sin(pix)}cos(pix)pisin(pix) - p^{2}i^{2}e^{sin(pix)}cos(pix)pi\\=&p^{3}i^{3}e^{sin(pix)}cos^{3}(pix) - 3p^{3}i^{3}e^{sin(pix)}sin(pix)cos(pix) - p^{3}i^{3}e^{sin(pix)}cos(pix)\\ \end{split}\end{equation} \]

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