There are 1 questions in this calculation: for each question, the 1 derivative of w is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (w - c)(u + \frac{a(sqrt(\frac{(p - w)}{w}) - sqrt(\frac{w}{(p - w)}))}{2})\ with\ respect\ to\ w：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = uw + \frac{1}{2}awsqrt(\frac{p}{w} - 1) - \frac{1}{2}awsqrt(\frac{w}{(p - w)}) - cu - \frac{1}{2}casqrt(\frac{p}{w} - 1) + \frac{1}{2}casqrt(\frac{w}{(p - w)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( uw + \frac{1}{2}awsqrt(\frac{p}{w} - 1) - \frac{1}{2}awsqrt(\frac{w}{(p - w)}) - cu - \frac{1}{2}casqrt(\frac{p}{w} - 1) + \frac{1}{2}casqrt(\frac{w}{(p - w)})\right)}{dw}\\=&u + \frac{1}{2}asqrt(\frac{p}{w} - 1) + \frac{\frac{1}{2}aw(\frac{p*-1}{w^{2}} + 0)*\frac{1}{2}}{(\frac{p}{w} - 1)^{\frac{1}{2}}} - \frac{1}{2}asqrt(\frac{w}{(p - w)}) - \frac{\frac{1}{2}aw((\frac{-(0 - 1)}{(p - w)^{2}})w + \frac{1}{(p - w)})*\frac{1}{2}}{(\frac{w}{(p - w)})^{\frac{1}{2}}} + 0 - \frac{\frac{1}{2}ca(\frac{p*-1}{w^{2}} + 0)*\frac{1}{2}}{(\frac{p}{w} - 1)^{\frac{1}{2}}} + \frac{\frac{1}{2}ca((\frac{-(0 - 1)}{(p - w)^{2}})w + \frac{1}{(p - w)})*\frac{1}{2}}{(\frac{w}{(p - w)})^{\frac{1}{2}}}\\=&u + \frac{asqrt(\frac{p}{w} - 1)}{2} - \frac{ap}{4(\frac{p}{w} - 1)^{\frac{1}{2}}w} - \frac{asqrt(\frac{w}{(p - w)})}{2} - \frac{aw^{\frac{3}{2}}}{4(p - w)^{\frac{3}{2}}} - \frac{aw^{\frac{1}{2}}}{4(p - w)^{\frac{1}{2}}} + \frac{cap}{4(\frac{p}{w} - 1)^{\frac{1}{2}}w^{2}} + \frac{caw^{\frac{1}{2}}}{4(p - w)^{\frac{3}{2}}} + \frac{ca}{4(p - w)^{\frac{1}{2}}w^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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