There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(x) - (\frac{(2x - 2)}{(x + 1)}) - (\frac{({(x - 1)}^{3})}{(6{x}^{3} + 6{x}^{2})})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x) - \frac{2x}{(x + 1)} - \frac{x^{3}}{(6x^{3} + 6x^{2})} + \frac{3x^{2}}{(6x^{3} + 6x^{2})} - \frac{3x}{(6x^{3} + 6x^{2})} + \frac{2}{(x + 1)} + \frac{1}{(6x^{3} + 6x^{2})}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( ln(x) - \frac{2x}{(x + 1)} - \frac{x^{3}}{(6x^{3} + 6x^{2})} + \frac{3x^{2}}{(6x^{3} + 6x^{2})} - \frac{3x}{(6x^{3} + 6x^{2})} + \frac{2}{(x + 1)} + \frac{1}{(6x^{3} + 6x^{2})}\right)}{dx}\\=&\frac{1}{(x)} - 2(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{2}{(x + 1)} - (\frac{-(6*3x^{2} + 6*2x)}{(6x^{3} + 6x^{2})^{2}})x^{3} - \frac{3x^{2}}{(6x^{3} + 6x^{2})} + 3(\frac{-(6*3x^{2} + 6*2x)}{(6x^{3} + 6x^{2})^{2}})x^{2} + \frac{3*2x}{(6x^{3} + 6x^{2})} - 3(\frac{-(6*3x^{2} + 6*2x)}{(6x^{3} + 6x^{2})^{2}})x - \frac{3}{(6x^{3} + 6x^{2})} + 2(\frac{-(1 + 0)}{(x + 1)^{2}}) + (\frac{-(6*3x^{2} + 6*2x)}{(6x^{3} + 6x^{2})^{2}})\\=&\frac{1}{x} + \frac{2x}{(x + 1)^{2}} - \frac{3x^{2}}{(6x^{3} + 6x^{2})} + \frac{18x^{5}}{(6x^{3} + 6x^{2})^{2}} - \frac{42x^{4}}{(6x^{3} + 6x^{2})^{2}} + \frac{6x}{(6x^{3} + 6x^{2})} + \frac{18x^{3}}{(6x^{3} + 6x^{2})^{2}} + \frac{18x^{2}}{(6x^{3} + 6x^{2})^{2}} - \frac{12x}{(6x^{3} + 6x^{2})^{2}} - \frac{3}{(6x^{3} + 6x^{2})} - \frac{2}{(x + 1)} - \frac{2}{(x + 1)^{2}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!