ans

023644
证明略

019070
(1) $f'(x)=2x\sin x+x^2 \cos x$; (2) $f'(x)=\dfrac{x^2+4x}{(x+2)^2}$; (3) $f'(x)=2x-4$

019071
证明略

019073
$-4$或$\dfrac{1}{4}$

019074
$-1$

009913
(1) $3\mathrm{e}^x-\mathrm{e}x^{\mathrm{e}-1}$; (2) $-\sin x+\dfrac{2}{x^2}$; (3) $24x^2+24x+6$; (4) $\dfrac{1}{2}x^{-\frac{1}{2}}\sin x+\sqrt{x} \cos x$; (5) $\ln x+1+2x^{-3}$; (6) $1+\dfrac{1}{x^2}$; (7) $\dfrac{4x}{(x^2+1)^2}$; (8) $\dfrac{1}{\cos^2 x}$

019076
证明略

000143
(1) $\sqrt{58}$; (2) $k=-\dfrac{1}{3}$, 反向

000144
(1) $\overrightarrow{AB}=(-9,15)$, $|\overrightarrow{AB}|=3\sqrt{34}$; (2) $\overrightarrow{OC}=(3,6)$, $\overrightarrow{OD}=(19,-39)$; (3) $-56$

000146
$\lambda=1$, $\mu=-2$

000148
$(\dfrac{1}{3},-\dfrac{5}{3})$

000149
证明略

000152
(1) 证明略; (2) $\dfrac{\pi}{6}$或$\dfrac{7\pi}{6}$

000155
$k=-\dfrac{2}{3}$

000157
证明略

000160
不存在

024842
$1$

014777
$\mathrm{e}$

024843
$2x\cos x-x^2 \sin x$

024844
$(1,-8)$或$(-1,-12)$

024845
$y=2\sqrt{2}x-1$或$y=-2\sqrt{2} x-1$

024846
$1+\sqrt{2}$

024847
$3$或$-1$

024849
$-\dfrac{8}{15}{}^\circ/\mathrm{min}$

041168
$-6-3\Delta t$

041170
\textcircled{3}

041171
等于

041173
$2$

041174
$-\dfrac{1}{2}$

041175
$\dfrac{1}{3}\text{m/s}$

041176
$-2$

023654
$\dfrac{10}{3}$

041191
$3$

041192
$-4$

041193
$y=x+1$与$y=-3x-3$

041194
$\dfrac{3}{4}$

041177
$\sqrt{2}$

041178
(1) $y=-2x+1$; (2) $y=x-\dfrac{1}{4}$

024850
(1) $f'(x)=\mathrm{e}^x-\cos x$; (2) $f'(x)=-\dfrac{1}{x\ln 3}$; (3) $f'(x)=2\sin x\cos x$; (4) $f'(x)=\dfrac{1}{\cos^2 x}$; (5) $f'(x)=-\dfrac{\cos x}{\sin^2 x}$; (6) $f'(x)=\dfrac{1}{2}x^{-\frac{1}{2}}-x^{-2}$; (7) $f'(x)=3x^2+6x+3$; (8) $f'(x)=\dfrac{1}{x}$

041197
(1) $y'=\dfrac{\sin x-\cos x-1}{(1+\cos x)^2}$; (2) $y'=3x^2-\dfrac{3}{x}x^{-\frac{5}{2}}+\dfrac{\cos x}{x^2}-\dfrac{2\in x}{x^3}$; (3) $y'=\dfrac{4}{(1-x)^2}$; (4) $y'=\tan x+\dfrac{x}{\cos^2 x}$