Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 1 derivative of n is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{n}^{2}}{(An + B{n}^{2} + C{n}^{3} + D{n}^{4} + e{n}^{5})}\ with\ respect\ to\ n:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{n^{2}}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{n^{2}}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)}\right)}{dn}\\=&(\frac{-(A + B*2n + C*3n^{2} + D*4n^{3} + 5n^{4}e + n^{5}*0)}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)^{2}})n^{2} + \frac{2n}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)}\\=&\frac{-An^{2}}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)^{2}} - \frac{2Bn^{3}}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)^{2}} - \frac{3Cn^{4}}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)^{2}} - \frac{4Dn^{5}}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)^{2}} - \frac{5n^{6}e}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)^{2}} + \frac{2n}{(An + Bn^{2} + Cn^{3} + Dn^{4} + n^{5}e)}\\ \end{split}\end{equation} \]





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