There are 1 questions in this calculation: for each question, the 4 derivative of p is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(p + q + r)}^{4}\ with\ respect\ to\ p：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = p^{4} + 4qp^{3} + 4rp^{3} + 6q^{2}p^{2} + 12qrp^{2} + 6r^{2}p^{2} + 4q^{3}p + 12q^{2}rp + 12qr^{2}p + 4r^{3}p + 4q^{3}r + 6q^{2}r^{2} + 4qr^{3} + q^{4} + r^{4}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( p^{4} + 4qp^{3} + 4rp^{3} + 6q^{2}p^{2} + 12qrp^{2} + 6r^{2}p^{2} + 4q^{3}p + 12q^{2}rp + 12qr^{2}p + 4r^{3}p + 4q^{3}r + 6q^{2}r^{2} + 4qr^{3} + q^{4} + r^{4}\right)}{dp}\\=&4p^{3} + 4q*3p^{2} + 4r*3p^{2} + 6q^{2}*2p + 12qr*2p + 6r^{2}*2p + 4q^{3} + 12q^{2}r + 12qr^{2} + 4r^{3} + 0 + 0 + 0 + 0 + 0\\=&4p^{3} + 12qp^{2} + 12rp^{2} + 12q^{2}p + 24qrp + 12r^{2}p + 12q^{2}r + 12qr^{2} + 4q^{3} + 4r^{3}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4p^{3} + 12qp^{2} + 12rp^{2} + 12q^{2}p + 24qrp + 12r^{2}p + 12q^{2}r + 12qr^{2} + 4q^{3} + 4r^{3}\right)}{dp}\\=&4*3p^{2} + 12q*2p + 12r*2p + 12q^{2} + 24qr + 12r^{2} + 0 + 0 + 0 + 0\\=&12p^{2} + 24qp + 24rp + 24qr + 12q^{2} + 12r^{2}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12p^{2} + 24qp + 24rp + 24qr + 12q^{2} + 12r^{2}\right)}{dp}\\=&12*2p + 24q + 24r + 0 + 0 + 0\\=&24p + 24q + 24r\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24p + 24q + 24r\right)}{dp}\\=&24 + 0 + 0\\=&24\\ \end{split}\end{equation} \]

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