There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ xln(x) + (2 - x)ln(2 - x) + \frac{a{x}^{2}}{2} + \frac{b{(x - 1)}^{4}}{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = xln(x) + 2ln(-x + 2) - xln(-x + 2) + \frac{1}{2}ax^{2} + \frac{1}{4}bx^{4} - bx^{3} + \frac{3}{2}bx^{2} - bx + \frac{1}{4}b\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xln(x) + 2ln(-x + 2) - xln(-x + 2) + \frac{1}{2}ax^{2} + \frac{1}{4}bx^{4} - bx^{3} + \frac{3}{2}bx^{2} - bx + \frac{1}{4}b\right)}{dx}\\=&ln(x) + \frac{x}{(x)} + \frac{2(-1 + 0)}{(-x + 2)} - ln(-x + 2) - \frac{x(-1 + 0)}{(-x + 2)} + \frac{1}{2}a*2x + \frac{1}{4}b*4x^{3} - b*3x^{2} + \frac{3}{2}b*2x - b + 0\\=&ln(x) + \frac{x}{(-x + 2)} - ln(-x + 2) - \frac{2}{(-x + 2)} + ax + bx^{3} - 3bx^{2} + 3bx - b + 1\\ \end{split}\end{equation} \]

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