There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ log_{\frac{1}{2}}^{{x}^{2} + 4x + 5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = log_{\frac{1}{2}}^{x^{2} + 4x + 5}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{\frac{1}{2}}^{x^{2} + 4x + 5}\right)}{dx}\\=&(\frac{(\frac{(2x + 4 + 0)}{(x^{2} + 4x + 5)} - \frac{(0)log_{\frac{1}{2}}^{x^{2} + 4x + 5}}{(\frac{1}{2})})}{(ln(\frac{1}{2}))})\\=&\frac{2x}{(x^{2} + 4x + 5)ln(\frac{1}{2})} + \frac{4}{(x^{2} + 4x + 5)ln(\frac{1}{2})}\\ \end{split}\end{equation} \]

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