There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 7{(x + {(7x + {(7x)}^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 7(x + (7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 7(x + (7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}\right)}{dx}\\=&7(\frac{\frac{1}{2}(1 + (\frac{\frac{1}{2}(7 + \frac{7^{\frac{1}{2}}*\frac{1}{2}}{x^{\frac{1}{2}}})}{(7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}}}))}{(x + (7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}})\\=&\frac{7*7^{\frac{1}{2}}}{8(x + (7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}(7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}}x^{\frac{1}{2}}} + \frac{49}{4(7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}}(x + (7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}} + \frac{7}{2(x + (7x + 7^{\frac{1}{2}}x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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