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

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