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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (a{x}^{2} + (2a + b)x + b)e^{x}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ax^{2}e^{x} + 2axe^{x} + bxe^{x} + be^{x}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( ax^{2}e^{x} + 2axe^{x} + bxe^{x} + be^{x}\right)}{dx}\\=&a*2xe^{x} + ax^{2}e^{x} + 2ae^{x} + 2axe^{x} + be^{x} + bxe^{x} + be^{x}\\=&4axe^{x} + ax^{2}e^{x} + 2ae^{x} + 2be^{x} + bxe^{x}\\ \end{split}\end{equation} \]





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