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

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