本次共计算 1 个题目:每一题对 x 求 1 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数sqrt(({x}^{2} + sqrt(3)x + \frac{3}{4})(36 - {x}^{2} + x - \frac{1}{4})) 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( sqrt(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})\right)}{dx}\\=&\frac{(-3x^{2}sqrt(3) - x^{3}*0*\frac{1}{2}*3^{\frac{1}{2}} + \frac{143}{4}sqrt(3) + \frac{143}{4}x*0*\frac{1}{2}*3^{\frac{1}{2}} + 2xsqrt(3) + x^{2}*0*\frac{1}{2}*3^{\frac{1}{2}} - 4x^{3} + 3x^{2} + 35*2x + \frac{3}{4} + 0)*\frac{1}{2}}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}}\\=&\frac{-3x^{2}sqrt(3)}{2(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{143sqrt(3)}{8(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{xsqrt(3)}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} - \frac{2x^{3}}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{3x^{2}}{2(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{35x}{(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}} + \frac{3}{8(-x^{3}sqrt(3) + \frac{143}{4}xsqrt(3) + x^{2}sqrt(3) - x^{4} + x^{3} + 35x^{2} + \frac{3}{4}x + \frac{429}{16})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!