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