There are 1 questions in this calculation: for each question, the 1 derivative of r is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 - {\frac{1}{(1 + r)}}^{T})}{r} + F{\frac{1}{(1 + r)}}^{T}\ with\ respect\ to\ r：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{{\frac{1}{(r + 1)}}^{T}}{r} + \frac{1}{r} + F{\frac{1}{(r + 1)}}^{T}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{{\frac{1}{(r + 1)}}^{T}}{r} + \frac{1}{r} + F{\frac{1}{(r + 1)}}^{T}\right)}{dr}\\=& - \frac{-{\frac{1}{(r + 1)}}^{T}}{r^{2}} - \frac{({\frac{1}{(r + 1)}}^{T}((0)ln(\frac{1}{(r + 1)}) + \frac{(T)((\frac{-(1 + 0)}{(r + 1)^{2}}))}{(\frac{1}{(r + 1)})}))}{r} + \frac{-1}{r^{2}} + F({\frac{1}{(r + 1)}}^{T}((0)ln(\frac{1}{(r + 1)}) + \frac{(T)((\frac{-(1 + 0)}{(r + 1)^{2}}))}{(\frac{1}{(r + 1)})}))\\=&\frac{{\frac{1}{(r + 1)}}^{T}}{r^{2}} + \frac{T{\frac{1}{(r + 1)}}^{T}}{(r + 1)r} - \frac{1}{r^{2}} - \frac{TF{\frac{1}{(r + 1)}}^{T}}{(r + 1)}\\ \end{split}\end{equation} \]

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