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 T is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(h{w}^{2})}{({e}^{(\frac{hw}{(kT)})} - 1)}\ with\ respect\ to\ T:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{hw^{2}}{({e}^{(\frac{hw}{kT})} - 1)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{hw^{2}}{({e}^{(\frac{hw}{kT})} - 1)}\right)}{dT}\\=&(\frac{-(({e}^{(\frac{hw}{kT})}((\frac{hw*-1}{kT^{2}})ln(e) + \frac{(\frac{hw}{kT})(0)}{(e)})) + 0)}{({e}^{(\frac{hw}{kT})} - 1)^{2}})hw^{2} + 0\\=&\frac{h^{2}w^{3}{e}^{(\frac{hw}{kT})}}{({e}^{(\frac{hw}{kT})} - 1)^{2}kT^{2}}\\ \end{split}\end{equation} \]





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