There are 1 questions in this calculation: for each question, the 1 derivative of T is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(({(2cosh(\frac{jT}{k}))}^{N})(1 + {(tanh(\frac{jT}{k}))}^{N}))\ with\ respect\ to\ T：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln((2cosh(\frac{jT}{k}))^{N}{tanh(\frac{jT}{k})}^{N} + (2cosh(\frac{jT}{k}))^{N})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln((2cosh(\frac{jT}{k}))^{N}{tanh(\frac{jT}{k})}^{N} + (2cosh(\frac{jT}{k}))^{N})\right)}{dT}\\=&\frac{(((2cosh(\frac{jT}{k}))^{N}((0)ln(2cosh(\frac{jT}{k})) + \frac{(N)(\frac{2sinh(\frac{jT}{k})j}{k})}{(2cosh(\frac{jT}{k}))})){tanh(\frac{jT}{k})}^{N} + (2cosh(\frac{jT}{k}))^{N}({tanh(\frac{jT}{k})}^{N}((0)ln(tanh(\frac{jT}{k})) + \frac{(N)(\frac{sech^{2}(\frac{jT}{k})j}{k})}{(tanh(\frac{jT}{k}))})) + ((2cosh(\frac{jT}{k}))^{N}((0)ln(2cosh(\frac{jT}{k})) + \frac{(N)(\frac{2sinh(\frac{jT}{k})j}{k})}{(2cosh(\frac{jT}{k}))})))}{((2cosh(\frac{jT}{k}))^{N}{tanh(\frac{jT}{k})}^{N} + (2cosh(\frac{jT}{k}))^{N})}\\=&\frac{jN(2cosh(\frac{jT}{k}))^{N}{tanh(\frac{jT}{k})}^{N}sinh(\frac{jT}{k})}{((2cosh(\frac{jT}{k}))^{N}{tanh(\frac{jT}{k})}^{N} + (2cosh(\frac{jT}{k}))^{N})kcosh(\frac{jT}{k})} + \frac{jN{tanh(\frac{jT}{k})}^{N}(2cosh(\frac{jT}{k}))^{N}sech^{2}(\frac{jT}{k})}{((2cosh(\frac{jT}{k}))^{N}{tanh(\frac{jT}{k})}^{N} + (2cosh(\frac{jT}{k}))^{N})ktanh(\frac{jT}{k})} + \frac{jN(2cosh(\frac{jT}{k}))^{N}sinh(\frac{jT}{k})}{((2cosh(\frac{jT}{k}))^{N}{tanh(\frac{jT}{k})}^{N} + (2cosh(\frac{jT}{k}))^{N})kcosh(\frac{jT}{k})}\\ \end{split}\end{equation} \]

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