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 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(sqrt({a}^{2} - {x}^{2}))}{30} + \frac{(b - x)}{60}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{30}sqrt(a^{2} - x^{2}) + \frac{1}{60}b - \frac{1}{60}x\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{1}{30}sqrt(a^{2} - x^{2}) + \frac{1}{60}b - \frac{1}{60}x\right)}{dx}\\=&\frac{\frac{1}{30}(0 - 2x)*\frac{1}{2}}{(a^{2} - x^{2})^{\frac{1}{2}}} + 0 - \frac{1}{60}\\=& - \frac{x}{30(a^{2} - x^{2})^{\frac{1}{2}}} - \frac{1}{60}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{x}{30(a^{2} - x^{2})^{\frac{1}{2}}} - \frac{1}{60}\right)}{dx}\\=& - \frac{(\frac{\frac{-1}{2}(0 - 2x)}{(a^{2} - x^{2})^{\frac{3}{2}}})x}{30} - \frac{1}{30(a^{2} - x^{2})^{\frac{1}{2}}} + 0\\=& - \frac{x^{2}}{30(a^{2} - x^{2})^{\frac{3}{2}}} - \frac{1}{30(a^{2} - x^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]





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