There are 1 questions in this calculation: for each question, the 4 derivative of p is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(p + q + r + s + t)}^{4}\ with\ respect\ to\ p：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = p^{4} + 4qp^{3} + 4rp^{3} + 4sp^{3} + 4tp^{3} + 6q^{2}p^{2} + 12qrp^{2} + 12qsp^{2} + 12qtp^{2} + 6r^{2}p^{2} + 12rsp^{2} + 12rtp^{2} + 6s^{2}p^{2} + 12stp^{2} + 6t^{2}p^{2} + 4q^{3}p + 12q^{2}rp + 12q^{2}sp + 12q^{2}tp + 12qr^{2}p + 24qrsp + 24qrtp + 12qs^{2}p + 24qstp + 12qt^{2}p + 4r^{3}p + 12r^{2}sp + 12r^{2}tp + 12rs^{2}p + 24rstp + 12rt^{2}p + 4s^{3}p + 12s^{2}tp + 12st^{2}p + 4t^{3}p + 24qrst + 12q^{2}st + 4q^{3}t + 12q^{2}rt + 12qr^{2}s + 12qr^{2}t + 12qs^{2}t + 12qst^{2} + 6q^{2}t^{2} + 12qrs^{2} + 12q^{2}rs + 12qrt^{2} + 4qr^{3} + 4q^{3}r + 6q^{2}r^{2} + 4qs^{3} + 6q^{2}s^{2} + 4q^{3}s + 4qt^{3} + q^{4} + 12r^{2}st + 4r^{3}t + 12rs^{2}t + 12rst^{2} + 6r^{2}t^{2} + 4rs^{3} + 6r^{2}s^{2} + 4r^{3}s + 4rt^{3} + r^{4} + 4s^{3}t + 6s^{2}t^{2} + 4st^{3} + s^{4} + t^{4}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( p^{4} + 4qp^{3} + 4rp^{3} + 4sp^{3} + 4tp^{3} + 6q^{2}p^{2} + 12qrp^{2} + 12qsp^{2} + 12qtp^{2} + 6r^{2}p^{2} + 12rsp^{2} + 12rtp^{2} + 6s^{2}p^{2} + 12stp^{2} + 6t^{2}p^{2} + 4q^{3}p + 12q^{2}rp + 12q^{2}sp + 12q^{2}tp + 12qr^{2}p + 24qrsp + 24qrtp + 12qs^{2}p + 24qstp + 12qt^{2}p + 4r^{3}p + 12r^{2}sp + 12r^{2}tp + 12rs^{2}p + 24rstp + 12rt^{2}p + 4s^{3}p + 12s^{2}tp + 12st^{2}p + 4t^{3}p + 24qrst + 12q^{2}st + 4q^{3}t + 12q^{2}rt + 12qr^{2}s + 12qr^{2}t + 12qs^{2}t + 12qst^{2} + 6q^{2}t^{2} + 12qrs^{2} + 12q^{2}rs + 12qrt^{2} + 4qr^{3} + 4q^{3}r + 6q^{2}r^{2} + 4qs^{3} + 6q^{2}s^{2} + 4q^{3}s + 4qt^{3} + q^{4} + 12r^{2}st + 4r^{3}t + 12rs^{2}t + 12rst^{2} + 6r^{2}t^{2} + 4rs^{3} + 6r^{2}s^{2} + 4r^{3}s + 4rt^{3} + r^{4} + 4s^{3}t + 6s^{2}t^{2} + 4st^{3} + s^{4} + t^{4}\right)}{dp}\\=&4p^{3} + 4q*3p^{2} + 4r*3p^{2} + 4s*3p^{2} + 4t*3p^{2} + 6q^{2}*2p + 12qr*2p + 12qs*2p + 12qt*2p + 6r^{2}*2p + 12rs*2p + 12rt*2p + 6s^{2}*2p + 12st*2p + 6t^{2}*2p + 4q^{3} + 12q^{2}r + 12q^{2}s + 12q^{2}t + 12qr^{2} + 24qrs + 24qrt + 12qs^{2} + 24qst + 12qt^{2} + 4r^{3} + 12r^{2}s + 12r^{2}t + 12rs^{2} + 24rst + 12rt^{2} + 4s^{3} + 12s^{2}t + 12st^{2} + 4t^{3} + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0\\=&4p^{3} + 12qp^{2} + 12rp^{2} + 12sp^{2} + 12tp^{2} + 12q^{2}p + 24qrp + 24qsp + 24qtp + 12r^{2}p + 24rsp + 24rtp + 12s^{2}p + 24stp + 12t^{2}p + 24qrs + 24qst + 12q^{2}t + 24qrt + 12q^{2}r + 12qr^{2} + 12qs^{2} + 12q^{2}s + 12qt^{2} + 4q^{3} + 24rst + 12r^{2}t + 12rs^{2} + 12r^{2}s + 12rt^{2} + 4r^{3} + 12s^{2}t + 12st^{2} + 4s^{3} + 4t^{3}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4p^{3} + 12qp^{2} + 12rp^{2} + 12sp^{2} + 12tp^{2} + 12q^{2}p + 24qrp + 24qsp + 24qtp + 12r^{2}p + 24rsp + 24rtp + 12s^{2}p + 24stp + 12t^{2}p + 24qrs + 24qst + 12q^{2}t + 24qrt + 12q^{2}r + 12qr^{2} + 12qs^{2} + 12q^{2}s + 12qt^{2} + 4q^{3} + 24rst + 12r^{2}t + 12rs^{2} + 12r^{2}s + 12rt^{2} + 4r^{3} + 12s^{2}t + 12st^{2} + 4s^{3} + 4t^{3}\right)}{dp}\\=&4*3p^{2} + 12q*2p + 12r*2p + 12s*2p + 12t*2p + 12q^{2} + 24qr + 24qs + 24qt + 12r^{2} + 24rs + 24rt + 12s^{2} + 24st + 12t^{2} + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0\\=&12p^{2} + 24qp + 24rp + 24sp + 24tp + 24qr + 24qs + 24qt + 12q^{2} + 24rs + 24rt + 12r^{2} + 24st + 12s^{2} + 12t^{2}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12p^{2} + 24qp + 24rp + 24sp + 24tp + 24qr + 24qs + 24qt + 12q^{2} + 24rs + 24rt + 12r^{2} + 24st + 12s^{2} + 12t^{2}\right)}{dp}\\=&12*2p + 24q + 24r + 24s + 24t + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0\\=&24p + 24q + 24r + 24s + 24t\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24p + 24q + 24r + 24s + 24t\right)}{dp}\\=&24 + 0 + 0 + 0 + 0\\=&24\\ \end{split}\end{equation} \]

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