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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(\frac{3}{2}x + 1050)}{(x + 300)}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{3}{2}x}{(x + 300)} + \frac{1050}{(x + 300)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{\frac{3}{2}x}{(x + 300)} + \frac{1050}{(x + 300)}\right)}{dx}\\=&\frac{3}{2}(\frac{-(1 + 0)}{(x + 300)^{2}})x + \frac{\frac{3}{2}}{(x + 300)} + 1050(\frac{-(1 + 0)}{(x + 300)^{2}})\\=&\frac{-3x}{2(x + 300)^{2}} - \frac{1050}{(x + 300)^{2}} + \frac{3}{2(x + 300)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3x}{2(x + 300)^{2}} - \frac{1050}{(x + 300)^{2}} + \frac{3}{2(x + 300)}\right)}{dx}\\=&\frac{-3(\frac{-2(1 + 0)}{(x + 300)^{3}})x}{2} - \frac{3}{2(x + 300)^{2}} - 1050(\frac{-2(1 + 0)}{(x + 300)^{3}}) + \frac{3(\frac{-(1 + 0)}{(x + 300)^{2}})}{2}\\=&\frac{3x}{(x + 300)^{3}} + \frac{2100}{(x + 300)^{3}} - \frac{3}{(x + 300)^{2}}\\ \end{split}\end{equation} \]





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