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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 + 0.2023x + 2.173{x}^{2})}{(1 + 0.1408x + 1.536{x}^{2})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{0.2023x}{(0.1408x + 1.536x + 1)} + \frac{2.173x^{2}}{(0.1408x + 1.536x + 1)} + \frac{1}{(0.1408x + 1.536x + 1)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{0.2023x}{(0.1408x + 1.536x + 1)} + \frac{2.173x^{2}}{(0.1408x + 1.536x + 1)} + \frac{1}{(0.1408x + 1.536x + 1)}\right)}{dx}\\=&0.2023(\frac{-(0.1408 + 1.536 + 0)}{(0.1408x + 1.536x + 1)^{2}})x + \frac{0.2023}{(0.1408x + 1.536x + 1)} + 2.173(\frac{-(0.1408 + 1.536 + 0)}{(0.1408x + 1.536x + 1)^{2}})x^{2} + \frac{2.173*2x}{(0.1408x + 1.536x + 1)} + (\frac{-(0.1408 + 1.536 + 0)}{(0.1408x + 1.536x + 1)^{2}})\\=&\frac{-0.33921664x}{(0.1408x + 1.536x + 1)(0.1408x + 1.536x + 1)} - \frac{3.6436864x^{2}}{(0.1408x + 1.536x + 1)(0.1408x + 1.536x + 1)} + \frac{4.346x}{(0.1408x + 1.536x + 1)} - \frac{1.6768}{(0.1408x + 1.536x + 1)(0.1408x + 1.536x + 1)} + \frac{0.2023}{(0.1408x + 1.536x + 1)}\\ \end{split}\end{equation} \]





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