There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{(({(x - 1)}^{3})({(x - 2)}^{\frac{1}{2}}))}{(({e}^{(3x)}){(x + 3)}^{\frac{1}{4}})})({x}^{x})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(x - 2)^{\frac{1}{2}}x^{3}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x^{2}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}x{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{(x - 2)^{\frac{1}{2}}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{(x - 2)^{\frac{1}{2}}x^{3}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x^{2}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}x{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{(x - 2)^{\frac{1}{2}}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}}\right)}{dx}\\=&\frac{(\frac{\frac{1}{2}(1 + 0)}{(x - 2)^{\frac{1}{2}}})x^{3}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} + (x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{4}(1 + 0)}{(x + 3)^{\frac{5}{4}}})x^{3}{e}^{(-3x)}{x}^{x} + \frac{(x - 2)^{\frac{1}{2}}*3x^{2}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} + \frac{(x - 2)^{\frac{1}{2}}x^{3}({e}^{(-3x)}((-3)ln(e) + \frac{(-3x)(0)}{(e)})){x}^{x}}{(x + 3)^{\frac{1}{4}}} + \frac{(x - 2)^{\frac{1}{2}}x^{3}{e}^{(-3x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{(x + 3)^{\frac{1}{4}}} - \frac{3(\frac{\frac{1}{2}(1 + 0)}{(x - 2)^{\frac{1}{2}}})x^{2}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - 3(x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{4}(1 + 0)}{(x + 3)^{\frac{5}{4}}})x^{2}{e}^{(-3x)}{x}^{x} - \frac{3(x - 2)^{\frac{1}{2}}*2x{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x^{2}({e}^{(-3x)}((-3)ln(e) + \frac{(-3x)(0)}{(e)})){x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x^{2}{e}^{(-3x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{(x + 3)^{\frac{1}{4}}} + \frac{3(\frac{\frac{1}{2}(1 + 0)}{(x - 2)^{\frac{1}{2}}})x{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} + 3(x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{4}(1 + 0)}{(x + 3)^{\frac{5}{4}}})x{e}^{(-3x)}{x}^{x} + \frac{3(x - 2)^{\frac{1}{2}}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}x({e}^{(-3x)}((-3)ln(e) + \frac{(-3x)(0)}{(e)})){x}^{x}}{(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}x{e}^{(-3x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{(x + 3)^{\frac{1}{4}}} - \frac{(\frac{\frac{1}{2}(1 + 0)}{(x - 2)^{\frac{1}{2}}}){e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - (x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{4}(1 + 0)}{(x + 3)^{\frac{5}{4}}}){e}^{(-3x)}{x}^{x} - \frac{(x - 2)^{\frac{1}{2}}({e}^{(-3x)}((-3)ln(e) + \frac{(-3x)(0)}{(e)})){x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{(x - 2)^{\frac{1}{2}}{e}^{(-3x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{(x + 3)^{\frac{1}{4}}}\\=&\frac{(x - 2)^{\frac{1}{2}}x^{3}{x}^{x}{e}^{(-3x)}ln(x)}{(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x^{2}{x}^{x}{e}^{(-3x)}ln(x)}{(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}x{x}^{x}{e}^{(-3x)}ln(x)}{(x + 3)^{\frac{1}{4}}} + \frac{x^{3}{e}^{(-3x)}{x}^{x}}{2(x - 2)^{\frac{1}{2}}(x + 3)^{\frac{1}{4}}} - \frac{(x - 2)^{\frac{1}{2}}x^{3}{e}^{(-3x)}{x}^{x}}{4(x + 3)^{\frac{5}{4}}} + \frac{12(x - 2)^{\frac{1}{2}}x^{2}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{3x^{2}{e}^{(-3x)}{x}^{x}}{2(x - 2)^{\frac{1}{2}}(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}x^{2}{e}^{(-3x)}{x}^{x}}{4(x + 3)^{\frac{5}{4}}} - \frac{15(x - 2)^{\frac{1}{2}}x{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x^{3}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x^{2}{x}^{x}{e}^{(-3x)}}{(x + 3)^{\frac{1}{4}}} + \frac{3x{e}^{(-3x)}{x}^{x}}{2(x - 2)^{\frac{1}{2}}(x + 3)^{\frac{1}{4}}} - \frac{3(x - 2)^{\frac{1}{2}}x{e}^{(-3x)}{x}^{x}}{4(x + 3)^{\frac{5}{4}}} - \frac{(x - 2)^{\frac{1}{2}}{x}^{x}{e}^{(-3x)}ln(x)}{(x + 3)^{\frac{1}{4}}} + \frac{(x - 2)^{\frac{1}{2}}x^{3}{x}^{x}{e}^{(-3x)}}{(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}x{x}^{x}{e}^{(-3x)}}{(x + 3)^{\frac{1}{4}}} - \frac{{e}^{(-3x)}{x}^{x}}{2(x - 2)^{\frac{1}{2}}(x + 3)^{\frac{1}{4}}} + \frac{(x - 2)^{\frac{1}{2}}{e}^{(-3x)}{x}^{x}}{4(x + 3)^{\frac{5}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} + \frac{3(x - 2)^{\frac{1}{2}}{e}^{(-3x)}{x}^{x}}{(x + 3)^{\frac{1}{4}}} - \frac{(x - 2)^{\frac{1}{2}}{x}^{x}{e}^{(-3x)}}{(x + 3)^{\frac{1}{4}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!