There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{{x}^{4}}{4} + 2{x}^{2} + 8x + 17)}^{\frac{1}{2}} - {(\frac{{x}^{4}}{4} - {x}^{2} + 4)}^{\frac{1}{2}}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{1}{4}x^{4} + 2x^{2} + 8x + 17)^{\frac{1}{2}} - (\frac{1}{4}x^{4} - x^{2} + 4)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( (\frac{1}{4}x^{4} + 2x^{2} + 8x + 17)^{\frac{1}{2}} - (\frac{1}{4}x^{4} - x^{2} + 4)^{\frac{1}{2}}\right)}{dx}\\=&(\frac{\frac{1}{2}(\frac{1}{4}*4x^{3} + 2*2x + 8 + 0)}{(\frac{1}{4}x^{4} + 2x^{2} + 8x + 17)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(\frac{1}{4}*4x^{3} - 2x + 0)}{(\frac{1}{4}x^{4} - x^{2} + 4)^{\frac{1}{2}}})\\=&\frac{x^{3}}{2(\frac{1}{4}x^{4} + 2x^{2} + 8x + 17)^{\frac{1}{2}}} + \frac{2x}{(\frac{1}{4}x^{4} + 2x^{2} + 8x + 17)^{\frac{1}{2}}} - \frac{x^{3}}{2(\frac{1}{4}x^{4} - x^{2} + 4)^{\frac{1}{2}}} + \frac{x}{(\frac{1}{4}x^{4} - x^{2} + 4)^{\frac{1}{2}}} + \frac{4}{(\frac{1}{4}x^{4} + 2x^{2} + 8x + 17)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!