There are 1 questions in this calculation: for each question, the 1 derivative of T is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ V*2((102.732 - \frac{(\frac{T}{t})}{1000} - 0.44{\frac{1}{(\frac{T}{t})}}^{1.22})tanh(4.5sqrt(\frac{T}{t})) - 102.6)\ with\ respect\ to\ T:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 205.464Vtanh(4.5sqrt(\frac{T}{t})) - \frac{0.002VTtanh(4.5sqrt(\frac{T}{t}))}{t} - \frac{0.88Vt^{\frac{61}{50}}tanh(4.5sqrt(\frac{T}{t}))}{T^{\frac{61}{50}}} - 205.2V\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 205.464Vtanh(4.5sqrt(\frac{T}{t})) - \frac{0.002VTtanh(4.5sqrt(\frac{T}{t}))}{t} - \frac{0.88Vt^{\frac{61}{50}}tanh(4.5sqrt(\frac{T}{t}))}{T^{\frac{61}{50}}} - 205.2V\right)}{dT}\\=&\frac{205.464Vsech^{2}(4.5sqrt(\frac{T}{t}))*4.5*0.5}{t(\frac{T}{t})^{\frac{1}{2}}} - \frac{0.002Vtanh(4.5sqrt(\frac{T}{t}))}{t} - \frac{0.002VTsech^{2}(4.5sqrt(\frac{T}{t}))*4.5*0.5}{tt(\frac{T}{t})^{\frac{1}{2}}} - \frac{0.88Vt^{\frac{61}{50}}*-1.22tanh(4.5sqrt(\frac{T}{t}))}{T^{\frac{111}{50}}} - \frac{0.88Vt^{\frac{61}{50}}sech^{2}(4.5sqrt(\frac{T}{t}))*4.5*0.5}{T^{\frac{61}{50}}t(\frac{T}{t})^{\frac{1}{2}}} + 0\\=&\frac{462.294Vsech^{2}(4.5sqrt(\frac{T}{t}))}{t^{\frac{1}{2}}T^{\frac{1}{2}}} - \frac{0.002Vtanh(4.5sqrt(\frac{T}{t}))}{t} - \frac{0.0045VT^{\frac{1}{2}}sech^{2}(4.5sqrt(\frac{T}{t}))}{t^{\frac{3}{2}}} + \frac{1.0736Vt^{\frac{61}{50}}tanh(4.5sqrt(\frac{T}{t}))}{T^{\frac{111}{50}}} - \frac{1.98Vt^{\frac{18}{25}}sech^{2}(4.5sqrt(\frac{T}{t}))}{T^{\frac{43}{25}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!