There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ A + \frac{(B - A)}{(1 + {10}^{((lg(10)(C) - x)D)})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = A + \frac{B}{({10}^{(CDlg(10) - Dx)} + 1)} - \frac{A}{({10}^{(CDlg(10) - Dx)} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( A + \frac{B}{({10}^{(CDlg(10) - Dx)} + 1)} - \frac{A}{({10}^{(CDlg(10) - Dx)} + 1)}\right)}{dx}\\=&0 + (\frac{-(({10}^{(CDlg(10) - Dx)}((\frac{CD*0}{ln{10}(10)} - D)ln(10) + \frac{(CDlg(10) - Dx)(0)}{(10)})) + 0)}{({10}^{(CDlg(10) - Dx)} + 1)^{2}})B + 0 - (\frac{-(({10}^{(CDlg(10) - Dx)}((\frac{CD*0}{ln{10}(10)} - D)ln(10) + \frac{(CDlg(10) - Dx)(0)}{(10)})) + 0)}{({10}^{(CDlg(10) - Dx)} + 1)^{2}})A + 0\\=&\frac{BD{10}^{(CDlg(10) - Dx)}ln(10)}{({10}^{(CDlg(10) - Dx)} + 1)^{2}} - \frac{AD{10}^{(CDlg(10) - Dx)}ln(10)}{({10}^{(CDlg(10) - Dx)} + 1)^{2}}\\ \end{split}\end{equation} \]

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