Mathematics
语言:中文
Language:English

current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(x + sqrt(1) + {x}^{2})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x + sqrt(1) + x^{2})\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( ln(x + sqrt(1) + x^{2})\right)}{dx}\\=&\frac{(1 + 0*\frac{1}{2}^{\frac{1}{2}} + 2x)}{(x + sqrt(1) + x^{2})}\\=&\frac{2x}{(x + sqrt(1) + x^{2})} + \frac{1}{(x + sqrt(1) + x^{2})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x}{(x + sqrt(1) + x^{2})} + \frac{1}{(x + sqrt(1) + x^{2})}\right)}{dx}\\=&2(\frac{-(1 + 0*\frac{1}{2}^{\frac{1}{2}} + 2x)}{(x + sqrt(1) + x^{2})^{2}})x + \frac{2}{(x + sqrt(1) + x^{2})} + (\frac{-(1 + 0*\frac{1}{2}^{\frac{1}{2}} + 2x)}{(x + sqrt(1) + x^{2})^{2}})\\=&\frac{-4x^{2}}{(x + sqrt(1) + x^{2})^{2}} - \frac{4x}{(x + sqrt(1) + x^{2})^{2}} + \frac{2}{(x + sqrt(1) + x^{2})} - \frac{1}{(x + sqrt(1) + x^{2})^{2}}\\ \end{split}\end{equation} \]





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


Return