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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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ de^{r}ivN((ln(x + sqrt(1 + {x}^{2}))}^{2})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = divNe^{r}ln(x + sqrt(x^{2} + 1))\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( divNe^{r}ln(x + sqrt(x^{2} + 1))\right)}{dx}\\=&divNe^{r}*0ln(x + sqrt(x^{2} + 1)) + \frac{divNe^{r}(1 + \frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}})}{(x + sqrt(x^{2} + 1))}\\=&\frac{divNe^{r}}{(x + sqrt(x^{2} + 1))} + \frac{divNxe^{r}}{(x + sqrt(x^{2} + 1))(x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{divNe^{r}}{(x + sqrt(x^{2} + 1))} + \frac{divNxe^{r}}{(x + sqrt(x^{2} + 1))(x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{-(1 + \frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}})}{(x + sqrt(x^{2} + 1))^{2}})divNe^{r} + \frac{divNe^{r}*0}{(x + sqrt(x^{2} + 1))} + \frac{(\frac{-(1 + \frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}})}{(x + sqrt(x^{2} + 1))^{2}})divNxe^{r}}{(x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{3}{2}}})divNxe^{r}}{(x + sqrt(x^{2} + 1))} + \frac{divNe^{r}}{(x + sqrt(x^{2} + 1))(x^{2} + 1)^{\frac{1}{2}}} + \frac{divNxe^{r}*0}{(x + sqrt(x^{2} + 1))(x^{2} + 1)^{\frac{1}{2}}}\\=& - \frac{2divNxe^{r}}{(x + sqrt(x^{2} + 1))^{2}(x^{2} + 1)^{\frac{1}{2}}} - \frac{divNe^{r}}{(x + sqrt(x^{2} + 1))^{2}} - \frac{divNx^{2}e^{r}}{(x + sqrt(x^{2} + 1))^{2}(x^{2} + 1)} - \frac{divNx^{2}e^{r}}{(x^{2} + 1)^{\frac{3}{2}}(x + sqrt(x^{2} + 1))} + \frac{divNe^{r}}{(x + sqrt(x^{2} + 1))(x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]





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