There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{2} + x + 11)sqrt({x}^{3} + 5x + 121)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}sqrt(x^{3} + 5x + 121) + xsqrt(x^{3} + 5x + 121) + 11sqrt(x^{3} + 5x + 121)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}sqrt(x^{3} + 5x + 121) + xsqrt(x^{3} + 5x + 121) + 11sqrt(x^{3} + 5x + 121)\right)}{dx}\\=&2xsqrt(x^{3} + 5x + 121) + \frac{x^{2}(3x^{2} + 5 + 0)*\frac{1}{2}}{(x^{3} + 5x + 121)^{\frac{1}{2}}} + sqrt(x^{3} + 5x + 121) + \frac{x(3x^{2} + 5 + 0)*\frac{1}{2}}{(x^{3} + 5x + 121)^{\frac{1}{2}}} + \frac{11(3x^{2} + 5 + 0)*\frac{1}{2}}{(x^{3} + 5x + 121)^{\frac{1}{2}}}\\=&2xsqrt(x^{3} + 5x + 121) + \frac{3x^{4}}{2(x^{3} + 5x + 121)^{\frac{1}{2}}} + \frac{19x^{2}}{(x^{3} + 5x + 121)^{\frac{1}{2}}} + sqrt(x^{3} + 5x + 121) + \frac{3x^{3}}{2(x^{3} + 5x + 121)^{\frac{1}{2}}} + \frac{5x}{2(x^{3} + 5x + 121)^{\frac{1}{2}}} + \frac{55}{2(x^{3} + 5x + 121)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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