There are 4 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/4]Find\ the\ first\ derivative\ of\ function\ {x}^{2} + 2x + 3\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2} + 2x + 3\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{2} + 2x + 3\right)}{dx}\\=&2x + 2 + 0\\=&2x + 2\\ \end{split}\end{equation} \]\[ \begin{equation}\begin{split}[2/4]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + 1)}{x}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x + \frac{1}{x}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x + \frac{1}{x}\right)}{dx}\\=&1 + \frac{-1}{x^{2}}\\=& - \frac{1}{x^{2}} + 1\\ \end{split}\end{equation} \]\[ \begin{equation}\begin{split}[3/4]Find\ the\ first\ derivative\ of\ function\ 3x - {x}^{3}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3x - x^{3}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 3x - x^{3}\right)}{dx}\\=&3 - 3x^{2}\\=& - 3x^{2} + 3\\ \end{split}\end{equation} \]\[ \begin{equation}\begin{split}[4/4]Find\ the\ first\ derivative\ of\ function\ {x}^{2}{e}^{x}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}{e}^{x}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{2}{e}^{x}\right)}{dx}\\=&2x{e}^{x} + x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&2x{e}^{x} + x^{2}{e}^{x}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!