123 lines
1.8 KiB
Plaintext
123 lines
1.8 KiB
Plaintext
ans
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023644
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证明略
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019070
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(1) $f'(x)=2x\sin x+x^2 \cos x$; (2) $f'(x)=\dfrac{x^2+4x}{(x+2)^2}$; (3) $f'(x)=2x-4$
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019071
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证明略
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019073
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$-4$或$\dfrac{1}{4}$
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019074
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$-1$
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009913
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(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) $\dfrac{1}{\cos^2 x}$
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019076
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证明略
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000143
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(1) $\sqrt{58}$; (2) $k=-\dfrac{1}{3}$, 反向
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000144
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(1) $\overrightarrow{AB}=(-9,15)$, $|\overrightarrow{AB}|=3\sqrt{34}$; (2) $\overrightarrow{OC}=(3,6)$, $\overrightarrow{OD}=(19,-39)$; (3) $-56$
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000146
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$\lambda=1$, $\mu=-2$
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000148
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$(\dfrac{1}{3},-\dfrac{5}{3})$
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000149
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证明略
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000152
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(1) 证明略; (2) $\dfrac{\pi}{6}$或$\dfrac{7\pi}{6}$
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000155
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$k=-\dfrac{2}{3}$
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000157
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证明略
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000160
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不存在
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024842
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$1$
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014777
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$\mathrm{e}$
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024843
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$2x\cos x-x^2 \sin x$
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024844
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$(1,-8)$或$(-1,-12)$
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024845
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$y=2\sqrt{2}x-1$或$y=-2\sqrt{2} x-1$
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024846
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$1+\sqrt{2}$
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024847
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$3$或$-1$
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024849
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$-\dfrac{8}{15}{}^\circ/\mathrm{min}$
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041168
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$-6-3\Delta t$
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041170
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\textcircled{3}
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041171
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等于
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041173
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$2$
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041174
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$-\dfrac{1}{2}$
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041175
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$\dfrac{1}{3}\text{m/s}$
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041176
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$-2$
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023654
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$\dfrac{10}{3}$
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041191
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$3$
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041192
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$-4$
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041193
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$y=x+1$与$y=-3x-3$
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041194
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$\dfrac{3}{4}$
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041177
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$\sqrt{2}$
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041178
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(1) $y=-2x+1$; (2) $y=x-\dfrac{1}{4}$
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024850
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(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) $f'(x)=\dfrac{1}{x}$
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041197
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(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) $y'=\tan x+\dfrac{x}{\cos^2 x}$
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