There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + {(x + {(x)}^{\frac{1}{4}})}^{\frac{1}{3}})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x + (x + x^{\frac{1}{4}})^{\frac{1}{3}})^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x + (x + x^{\frac{1}{4}})^{\frac{1}{3}})^{\frac{1}{2}}\right)}{dx}\\=&(\frac{\frac{1}{2}(1 + (\frac{\frac{1}{3}(1 + \frac{\frac{1}{4}}{x^{\frac{3}{4}}})}{(x + x^{\frac{1}{4}})^{\frac{2}{3}}}))}{(x + (x + x^{\frac{1}{4}})^{\frac{1}{3}})^{\frac{1}{2}}})\\=&\frac{1}{24(x + x^{\frac{1}{4}})^{\frac{2}{3}}(x + (x + x^{\frac{1}{4}})^{\frac{1}{3}})^{\frac{1}{2}}x^{\frac{3}{4}}} + \frac{1}{6(x + x^{\frac{1}{4}})^{\frac{2}{3}}(x + (x + x^{\frac{1}{4}})^{\frac{1}{3}})^{\frac{1}{2}}} + \frac{1}{2(x + (x + x^{\frac{1}{4}})^{\frac{1}{3}})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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