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

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