There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{1}{2})ln(sqrt(\frac{x}{2}) + sqrt((\frac{x}{2}) - 1)) - (\frac{1}{2})(1 - (\frac{2}{x})) + (\frac{1}{8}){(sqrt(1 - x))}^{4}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}ln(sqrt(\frac{1}{2}x) + sqrt(\frac{1}{2}x - 1)) + \frac{1}{x} + \frac{1}{8}sqrt(-x + 1)^{4} - \frac{1}{2}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{1}{2}ln(sqrt(\frac{1}{2}x) + sqrt(\frac{1}{2}x - 1)) + \frac{1}{x} + \frac{1}{8}sqrt(-x + 1)^{4} - \frac{1}{2}\right)}{dx}\\=&\frac{\frac{1}{2}(\frac{\frac{1}{2}*\frac{1}{2}}{(\frac{1}{2}x)^{\frac{1}{2}}} + \frac{(\frac{1}{2} + 0)*\frac{1}{2}}{(\frac{1}{2}x - 1)^{\frac{1}{2}}})}{(sqrt(\frac{1}{2}x) + sqrt(\frac{1}{2}x - 1))} + \frac{-1}{x^{2}} + \frac{\frac{1}{8}*4(-x + 1)^{\frac{3}{2}}(-1 + 0)*\frac{1}{2}}{(-x + 1)^{\frac{1}{2}}} + 0\\=&\frac{2^{\frac{1}{2}}}{8(sqrt(\frac{1}{2}x) + sqrt(\frac{1}{2}x - 1))x^{\frac{1}{2}}} + \frac{1}{8(sqrt(\frac{1}{2}x) + sqrt(\frac{1}{2}x - 1))(\frac{1}{2}x - 1)^{\frac{1}{2}}} - \frac{1}{x^{2}} + \frac{x}{4} - \frac{1}{4}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!