There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{x}^{1}{(x - 5)}^{5}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{6} - \frac{25}{2}x^{5} + 125x^{4} - 625x^{3} + \frac{3125}{2}x^{2} - \frac{3125}{2}x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{6} - \frac{25}{2}x^{5} + 125x^{4} - 625x^{3} + \frac{3125}{2}x^{2} - \frac{3125}{2}x\right)}{dx}\\=&\frac{1}{2}*6x^{5} - \frac{25}{2}*5x^{4} + 125*4x^{3} - 625*3x^{2} + \frac{3125}{2}*2x - \frac{3125}{2}\\=&3x^{5} - \frac{125x^{4}}{2} + 500x^{3} - 1875x^{2} + 3125x - \frac{3125}{2}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！