Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ 1 - arcsin(x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - arcsin(x) + 1\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - arcsin(x) + 1\right)}{dx}\\=& - (\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}) + 0\\=& - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=& - (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})\\=& - \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=& - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x - \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}}\\=& - \frac{3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]





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