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