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

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