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 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(16 - 5x)}{(x(x + 4))}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{5x}{(x^{2} + 4x)} + \frac{16}{(x^{2} + 4x)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - \frac{5x}{(x^{2} + 4x)} + \frac{16}{(x^{2} + 4x)}\right)}{dx}\\=& - 5(\frac{-(2x + 4)}{(x^{2} + 4x)^{2}})x - \frac{5}{(x^{2} + 4x)} + 16(\frac{-(2x + 4)}{(x^{2} + 4x)^{2}})\\=&\frac{10x^{2}}{(x^{2} + 4x)^{2}} - \frac{12x}{(x^{2} + 4x)^{2}} - \frac{5}{(x^{2} + 4x)} - \frac{64}{(x^{2} + 4x)^{2}}\\ \end{split}\end{equation} \]





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