There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sqrt(172225 - {(x - 1500)}^{2})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(-x^{2} + 3000x - 2077775)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sqrt(-x^{2} + 3000x - 2077775)\right)}{dx}\\=&\frac{(-2x + 3000 + 0)*\frac{1}{2}}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}}\\=&\frac{-x}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} + \frac{1500}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} + \frac{1500}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}}\right)}{dx}\\=&-(\frac{\frac{-1}{2}(-2x + 3000 + 0)}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}})x - \frac{1}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} + 1500(\frac{\frac{-1}{2}(-2x + 3000 + 0)}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}})\\=&\frac{-x^{2}}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}} + \frac{3000x}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}} - \frac{1}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} - \frac{2250000}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !