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

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