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