There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{3{(ln(x))}^{2}(1 - 2xln(x))}{(x{e}^{(6x)})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3{e}^{(-6x)}ln^{2}(x)}{x} - 6{e}^{(-6x)}ln^{3}(x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{3{e}^{(-6x)}ln^{2}(x)}{x} - 6{e}^{(-6x)}ln^{3}(x)\right)}{dx}\\=&\frac{3*-{e}^{(-6x)}ln^{2}(x)}{x^{2}} + \frac{3({e}^{(-6x)}((-6)ln(e) + \frac{(-6x)(0)}{(e)}))ln^{2}(x)}{x} + \frac{3{e}^{(-6x)}*2ln(x)}{x(x)} - 6({e}^{(-6x)}((-6)ln(e) + \frac{(-6x)(0)}{(e)}))ln^{3}(x) - \frac{6{e}^{(-6x)}*3ln^{2}(x)}{(x)}\\=&\frac{-3{e}^{(-6x)}ln^{2}(x)}{x^{2}} - \frac{36{e}^{(-6x)}ln^{2}(x)}{x} + \frac{6{e}^{(-6x)}ln(x)}{x^{2}} + 36{e}^{(-6x)}ln^{3}(x)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !