微积分学/导数/導數練習

求导数

$y=\frac{(2+5x{)}^{10}}{x}$ $\begin{array}{cc}{y}^{\prime }& =\left[\frac{(2+5x{)}^{10}}{x}\right]\\ & =-\frac{1}{x^2}(2+5x{)}^{10}+\frac{1}{x}\cdot 10(2+5x{)}^9\cdot 5\\ & =-\frac{(2+5x{)}^{10}}{x^2}+\frac{50(2+5x{)}^9}{x}\end{array}$

$y=x\cos (2x+\frac{\pi }{2})\sin (2x+\frac{\pi }{2})$ $y=x(-\sin 2x)\cos 2x=-\frac{1}{2}x\sin 4x$ $\begin{array}{cc}{y}^{\prime }& =(-\frac{1}{2}x\sin 4x)\\ & =-\frac{1}{2}\sin 4x-\frac{1}{2}x\cos 4x\cdot 4\\ & =-\frac{1}{2}\sin 4x-2x\cos 4x\\ \end{array}$