There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{({(a + b{x}^{2} + c{y}^{2})}^{2} + {(dy)}^{2})}^{1}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = abx^{2} + acy^{2} + \frac{1}{2}a^{2} + \frac{1}{2}b^{2}x^{4} + bcy^{2}x^{2} + \frac{1}{2}c^{2}y^{4} + \frac{1}{2}y^{2}d^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( abx^{2} + acy^{2} + \frac{1}{2}a^{2} + \frac{1}{2}b^{2}x^{4} + bcy^{2}x^{2} + \frac{1}{2}c^{2}y^{4} + \frac{1}{2}y^{2}d^{2}\right)}{dx}\\=&ab*2x + 0 + 0 + \frac{1}{2}b^{2}*4x^{3} + bcy^{2}*2x + 0 + 0\\=&2abx + 2b^{2}x^{3} + 2bcy^{2}x\\ \end{split}\end{equation} \]

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