There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt((48x - 48){\frac{1}{x}}^{2})sin(x)cos(x)tan(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(x)cos(x)tan(x)sqrt(\frac{48}{x} - \frac{48}{x^{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(x)cos(x)tan(x)sqrt(\frac{48}{x} - \frac{48}{x^{2}})\right)}{dx}\\=&cos(x)cos(x)tan(x)sqrt(\frac{48}{x} - \frac{48}{x^{2}}) + sin(x)*-sin(x)tan(x)sqrt(\frac{48}{x} - \frac{48}{x^{2}}) + sin(x)cos(x)sec^{2}(x)(1)sqrt(\frac{48}{x} - \frac{48}{x^{2}}) + \frac{sin(x)cos(x)tan(x)(\frac{48*-1}{x^{2}} - \frac{48*-2}{x^{3}})*\frac{1}{2}}{(\frac{48}{x} - \frac{48}{x^{2}})^{\frac{1}{2}}}\\=&cos^{2}(x)tan(x)sqrt(\frac{48}{x} - \frac{48}{x^{2}}) - sin^{2}(x)tan(x)sqrt(\frac{48}{x} - \frac{48}{x^{2}}) + sin(x)cos(x)sqrt(\frac{48}{x} - \frac{48}{x^{2}})sec^{2}(x) - \frac{24sin(x)cos(x)tan(x)}{(\frac{48}{x} - \frac{48}{x^{2}})^{\frac{1}{2}}x^{2}} + \frac{48sin(x)cos(x)tan(x)}{(\frac{48}{x} - \frac{48}{x^{2}})^{\frac{1}{2}}x^{3}}\\ \end{split}\end{equation} \]

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