本次共计算 1 个题目:每一题对 z 求 4 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数(3{z}^{2} - 4cz + {c}^{2})(1 - cos(z)) + (-{z}^{3} + 2c{z}^{2} - z{c}^{2})sin(z) 关于 z 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - 3z^{2}cos(z) - z^{3}sin(z) + 4czcos(z) + 2cz^{2}sin(z) - c^{2}cos(z) - c^{2}zsin(z) + 3z^{2} - 4cz + c^{2}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( - 3z^{2}cos(z) - z^{3}sin(z) + 4czcos(z) + 2cz^{2}sin(z) - c^{2}cos(z) - c^{2}zsin(z) + 3z^{2} - 4cz + c^{2}\right)}{dz}\\=& - 3*2zcos(z) - 3z^{2}*-sin(z) - 3z^{2}sin(z) - z^{3}cos(z) + 4ccos(z) + 4cz*-sin(z) + 2c*2zsin(z) + 2cz^{2}cos(z) - c^{2}*-sin(z) - c^{2}sin(z) - c^{2}zcos(z) + 3*2z - 4c + 0\\=& - 6zcos(z) - z^{3}cos(z) + 4ccos(z) + 2cz^{2}cos(z) - c^{2}zcos(z) + 6z - 4c\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( - 6zcos(z) - z^{3}cos(z) + 4ccos(z) + 2cz^{2}cos(z) - c^{2}zcos(z) + 6z - 4c\right)}{dz}\\=& - 6cos(z) - 6z*-sin(z) - 3z^{2}cos(z) - z^{3}*-sin(z) + 4c*-sin(z) + 2c*2zcos(z) + 2cz^{2}*-sin(z) - c^{2}cos(z) - c^{2}z*-sin(z) + 6 + 0\\=& - 6cos(z) + 6zsin(z) - 3z^{2}cos(z) + z^{3}sin(z) - 4csin(z) + 4czcos(z) - 2cz^{2}sin(z) - c^{2}cos(z) + c^{2}zsin(z) + 6\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( - 6cos(z) + 6zsin(z) - 3z^{2}cos(z) + z^{3}sin(z) - 4csin(z) + 4czcos(z) - 2cz^{2}sin(z) - c^{2}cos(z) + c^{2}zsin(z) + 6\right)}{dz}\\=& - 6*-sin(z) + 6sin(z) + 6zcos(z) - 3*2zcos(z) - 3z^{2}*-sin(z) + 3z^{2}sin(z) + z^{3}cos(z) - 4ccos(z) + 4ccos(z) + 4cz*-sin(z) - 2c*2zsin(z) - 2cz^{2}cos(z) - c^{2}*-sin(z) + c^{2}sin(z) + c^{2}zcos(z) + 0\\=&12sin(z) + 6z^{2}sin(z) + z^{3}cos(z) - 8czsin(z) - 2cz^{2}cos(z) + 2c^{2}sin(z) + c^{2}zcos(z)\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( 12sin(z) + 6z^{2}sin(z) + z^{3}cos(z) - 8czsin(z) - 2cz^{2}cos(z) + 2c^{2}sin(z) + c^{2}zcos(z)\right)}{dz}\\=&12cos(z) + 6*2zsin(z) + 6z^{2}cos(z) + 3z^{2}cos(z) + z^{3}*-sin(z) - 8csin(z) - 8czcos(z) - 2c*2zcos(z) - 2cz^{2}*-sin(z) + 2c^{2}cos(z) + c^{2}cos(z) + c^{2}z*-sin(z)\\=&12cos(z) + 12zsin(z) + 9z^{2}cos(z) - z^{3}sin(z) - 8csin(z) - 12czcos(z) + 2cz^{2}sin(z) + 3c^{2}cos(z) - c^{2}zsin(z)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!