There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 0.5x(1 + \frac{sinh(sqrt(\frac{2i(x + 0.044715{x}^{3})}{p}))}{cosh(sqrt(\frac{2i(x + 0.044715{x}^{3})}{p}))})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{0.5xsinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{cosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} + 0.5x\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{0.5xsinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{cosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} + 0.5x\right)}{dx}\\=&\frac{0.5sinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{cosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} + \frac{0.5xcosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))(\frac{2i}{p} + \frac{0.08943i}{p})*0.5}{(\frac{2ix}{p} + \frac{0.08943ix}{p})^{\frac{1}{2}}cosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} + \frac{0.5xsinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))*-sinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))(\frac{2i}{p} + \frac{0.08943i}{p})*0.5}{cosh^{2}(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))(\frac{2ix}{p} + \frac{0.08943ix}{p})^{\frac{1}{2}}} + 0.5\\=&\frac{0.5sinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{cosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} + \frac{0.5ixcosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{(\frac{2ix}{p} + \frac{0.08943ix}{p})^{\frac{1}{2}}pcosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} + \frac{0.0223575ixcosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{(\frac{2ix}{p} + \frac{0.08943ix}{p})^{\frac{1}{2}}pcosh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} - \frac{0.5ixsinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))sinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{(\frac{2ix}{p} + \frac{0.08943ix}{p})^{\frac{1}{2}}pcosh^{2}(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} - \frac{0.0223575ixsinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))sinh(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))}{(\frac{2ix}{p} + \frac{0.08943ix}{p})^{\frac{1}{2}}pcosh^{2}(sqrt(\frac{2ix}{p} + \frac{0.08943ix}{p}))} + 0.5\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!