There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ th(\frac{1}{2})sin(x) + log_{5x}^{100xx}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(x)th(\frac{1}{2}) + log_{5x}^{100x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(x)th(\frac{1}{2}) + log_{5x}^{100x^{2}}\right)}{dx}\\=&cos(x)th(\frac{1}{2}) + sin(x)(1 - th^{2}(\frac{1}{2}))*0 + (\frac{(\frac{(100*2x)}{(100x^{2})} - \frac{(5)log_{5x}^{100x^{2}}}{(5x)})}{(ln(5x))})\\=&cos(x)th(\frac{1}{2}) + \frac{2}{xln(5x)} - \frac{log_{5x}^{100x^{2}}}{xln(5x)}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！