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

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