There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {2}^{{(x + 1)}^{2}}ln(3x + 5)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {2}^{(x^{2} + 2x + 1)}ln(3x + 5)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {2}^{(x^{2} + 2x + 1)}ln(3x + 5)\right)}{dx}\\=&({2}^{(x^{2} + 2x + 1)}((2x + 2 + 0)ln(2) + \frac{(x^{2} + 2x + 1)(0)}{(2)}))ln(3x + 5) + \frac{{2}^{(x^{2} + 2x + 1)}(3 + 0)}{(3x + 5)}\\=&2x{2}^{(x^{2} + 2x + 1)}ln(2)ln(3x + 5) + 2 * {2}^{(x^{2} + 2x + 1)}ln(2)ln(3x + 5) + \frac{3 * {2}^{(x^{2} + 2x + 1)}}{(3x + 5)}\\ \end{split}\end{equation} \]

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