There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arcsin(x) + lg(x) - sin(x)cos({x}^{3})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(x) + lg(x) - sin(x)cos(x^{3})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(x) + lg(x) - sin(x)cos(x^{3})\right)}{dx}\\=&(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}) + \frac{1}{ln{10}(x)} - cos(x)cos(x^{3}) - sin(x)*-sin(x^{3})*3x^{2}\\=&\frac{1}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{1}{xln{10}} - cos(x)cos(x^{3}) + 3x^{2}sin(x^{3})sin(x)\\ \end{split}\end{equation} \]

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