举一反三
- 设 $f(\sin x)=\cos2x+1$，则 $f(\cos x)=$（ ）. A: $\cos^2x$ B: $-2\cos^2x$ C: $-2\sin^2x$ D: $2-2\cos^2x$
- 已知\( y = {x^3}\cos 2x \)，则\( y'' \)为（ ）. A: 0 B: \( 6x\cos 2x{\rm{ + }}12{x^2}\sin 2x - 4{x^3}\cos 2x \) C: \( 6x\cos 2x - 12{x^2}\sin 2x{\rm{ + }}4{x^3}\cos 2x \) D: \( 6x\cos 2x - 12{x^2}\sin 2x - 4{x^3}\cos 2x \)
- 曲线积分$$\int_{(0,0}^{(x,y)}(2x\cos y-y^2\sin x)dx+(2y\cos x-x^2\sin y)dy=$$ A: $y^2\cos x+x^2\cos y$ B: $x^2\cos x+y^2\cos y$ C: $x^2\sin y+y^2\sin x$ D: $x^2\sin x+y^2\sin y$
- 3. $(2x\cos y-{{y}^{2}}\sin x)dx+(2y\cos x-{{x}^{2}}\sin y)dy$的原函数是 ( ) A: ${{x}^{2}}\sin y-{{y}^{2}}\sin x+C$ B: ${{x}^{2}}\sin y+{{y}^{2}}\sin x+C$ C: ${{x}^{2}}\cos y-{{y}^{2}}\cos x+C$ D: ${{x}^{2}}\cos y+{{y}^{2}}\cos x+C$
- 函数\(y = \sin{x^2}\)的导数为( ). A: \( - 2x\sec {x^4}\) B: \(2x\cos {x^2}\) C: \(2x\sec {x^2}\) D: \(- 2x\sec {x^2}\)
内容
- 0
函数\(y = {\sin ^2}x\)的导数为（ ）. A: \(\cos 2x\) B: \(\sin 2x\) C: \( - \sin 2x\) D: \(- \cos 2x\)
- 1
2. 已知$f(x)$的一个原函数是$\sin x$，$g(x)$的一个原函数是${{x}^{2}}$，则复函数$f[g(x)]$的原函数是( ). A: $\frac{\sin 2x}{2}$ B: ${{\cos }^{2}}x$ C: $\cos {{x}^{2}}$ D: $\cos 2x$
- 2
【单选题】设y=sin(cos(x)),求 结果为:(本题10.0分) A. cos(cos(x))*cos(x)+ sin(cos(x))*sin(x)^2 B. - cos(cos(x))*cos(x) - sin(cos(x))*sin(x)^2 C. - cos(cos(x))*cos(x)^2 - sin(cos(x))*sin(x)^2 D. - cos(cos(x))*cos(x) ^2- sin(cos(x))*sin(x)
- 3
$\int {{1 \over {3 + 5\cos x}}} dx = \left( {} \right)$ A: ${1 \over 4}\ln \left| {{{2\cos x + \sin x} \over {2\cos x - \sin x}}} \right| + C$ B: ${1 \over 4}\ln \left| {{{2\cos {x \over 2} + \sin {x \over 2}} \over {2\cos {x \over 2} - \sin {x \over 2}}}} \right| + C$ C: $\ln \left| {{{\cos {x \over 2} + \sin {x \over 2}} \over {\cos {x \over 2} - \sin {x \over 2}}}} \right| + C$ D: $\ln \left| {{{\cos x + \sin x} \over {\cos x - \sin x}}} \right| + C$
- 4
常微分方程[img=243x26]1802e4d57c1aad8.png[/img]的解为： A: exp(-x)*sin(3^(1/2)*x)*C2+exp(-x)*cos(3^(1/2)*x)*C1-1/4*cos(2*x)，C1、C2为任意常数 B: exp(-2x)*cos(3^(1/2)*x)*C2+exp(-2x)*cos(3^(1/2)*x)*C1-1/4*sin(2*x)，C1、C2为任意常数 C: exp(-3x)*sin(3^(1/2)*x)*C2+exp(-3x)*sin(3^(1/2)*x)*C1-1/4*sin(2*x)，C1、C2为任意常数 D: exp(-4x)*sin(3^(1/2)*x)*C2-exp(-4x)*cos(3^(1/2)*x)*C1-1/4*cos(2*x)，C1、C2为任意常数