There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({R}^{2}(p + rgh) + \frac{xrg(3{R}^{2} - 3Rxtan(a) + {x}^{2}{tan(a)}^{2})}{3})}{(2(R - xtan(a))cos(a))}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{R^{2}p}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{R^{2}rgh}{(2Rcos(a) - 2xcos(a)tan(a))} - \frac{Rrgx^{2}tan(a)}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{R^{2}rgx}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{\frac{1}{3}rgx^{3}tan^{2}(a)}{(2Rcos(a) - 2xcos(a)tan(a))}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{R^{2}p}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{R^{2}rgh}{(2Rcos(a) - 2xcos(a)tan(a))} - \frac{Rrgx^{2}tan(a)}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{R^{2}rgx}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{\frac{1}{3}rgx^{3}tan^{2}(a)}{(2Rcos(a) - 2xcos(a)tan(a))}\right)}{dx}\\=&(\frac{-(2R*-sin(a)*0 - 2cos(a)tan(a) - 2x*-sin(a)*0tan(a) - 2xcos(a)sec^{2}(a)(0))}{(2Rcos(a) - 2xcos(a)tan(a))^{2}})R^{2}p + 0 + (\frac{-(2R*-sin(a)*0 - 2cos(a)tan(a) - 2x*-sin(a)*0tan(a) - 2xcos(a)sec^{2}(a)(0))}{(2Rcos(a) - 2xcos(a)tan(a))^{2}})R^{2}rgh + 0 - (\frac{-(2R*-sin(a)*0 - 2cos(a)tan(a) - 2x*-sin(a)*0tan(a) - 2xcos(a)sec^{2}(a)(0))}{(2Rcos(a) - 2xcos(a)tan(a))^{2}})Rrgx^{2}tan(a) - \frac{Rrg*2xtan(a)}{(2Rcos(a) - 2xcos(a)tan(a))} - \frac{Rrgx^{2}sec^{2}(a)(0)}{(2Rcos(a) - 2xcos(a)tan(a))} + (\frac{-(2R*-sin(a)*0 - 2cos(a)tan(a) - 2x*-sin(a)*0tan(a) - 2xcos(a)sec^{2}(a)(0))}{(2Rcos(a) - 2xcos(a)tan(a))^{2}})R^{2}rgx + \frac{R^{2}rg}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{1}{3}(\frac{-(2R*-sin(a)*0 - 2cos(a)tan(a) - 2x*-sin(a)*0tan(a) - 2xcos(a)sec^{2}(a)(0))}{(2Rcos(a) - 2xcos(a)tan(a))^{2}})rgx^{3}tan^{2}(a) + \frac{\frac{1}{3}rg*3x^{2}tan^{2}(a)}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{\frac{1}{3}rgx^{3}*2tan(a)sec^{2}(a)(0)}{(2Rcos(a) - 2xcos(a)tan(a))}\\=&\frac{2R^{2}pcos(a)tan(a)}{(2Rcos(a) - 2xcos(a)tan(a))^{2}} + \frac{2R^{2}rghcos(a)tan(a)}{(2Rcos(a) - 2xcos(a)tan(a))^{2}} - \frac{2Rrgx^{2}cos(a)tan^{2}(a)}{(2Rcos(a) - 2xcos(a)tan(a))^{2}} - \frac{2Rrgxtan(a)}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{2R^{2}rgxcos(a)tan(a)}{(2Rcos(a) - 2xcos(a)tan(a))^{2}} + \frac{R^{2}rg}{(2Rcos(a) - 2xcos(a)tan(a))} + \frac{2rgx^{3}cos(a)tan^{3}(a)}{3(2Rcos(a) - 2xcos(a)tan(a))^{2}} + \frac{rgx^{2}tan^{2}(a)}{(2Rcos(a) - 2xcos(a)tan(a))}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!