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

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