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

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