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

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