下列函数组线性无关的是( )
A: $\sin
2x, \sin x\cos x$
B: $\dfrac{\tan^2
x}{2}, \sec^2 x-1$
C: $\cot^2
x, \dfrac{\csc^2 x-1}{3}$
D: $e^{ax},
e^{bx} (a\neq b)$
A: $\sin
2x, \sin x\cos x$
B: $\dfrac{\tan^2
x}{2}, \sec^2 x-1$
C: $\cot^2
x, \dfrac{\csc^2 x-1}{3}$
D: $e^{ax},
e^{bx} (a\neq b)$
举一反三
- $\int {{{x\cos x} \over {{{\sin }^3}x}}} dx = \left( {} \right)$ A: $ - {x \over {2{{\sin }^2}x}} - {1 \over 2}\tan x + C$ B: $ - {x \over {2{{\sin }^2}x}} - {1 \over 2}\cot x + C$ C: $ - {x \over {2{{\cos }^2}x}} - {1 \over 2}\cot x + C$ D: $ - {x \over {2{{\cos }^2}x}} - {1 \over 2}\tan x + C$
- 求函数[img=192x40]17da653862ff7b6.png[/img]的导数； ( ) A: cos(x)/sin(x) - cot(x)*(cot(x)^2 + 1) B: cos(x)/sin(x) C: cot(x)*(cot(x)^2 + 1) D: cos(x)/sin(x) - cot(x)*(cot(x)^2 + 1)+cot(x)
- 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: \(- 2x\sec {x^2}\)
- 函数\(y<br/>= 1\)与\(y<br/>= {\sin ^2}x + {\cos ^2}x\)是相同的函数。（ ）
- \(\int { { {\sec }^{3}}xdx}\)=( ) A: \(\frac{1}{2}\sec x\cot x-\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) B: \(\frac{1}{2}\sec x\tan x+\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) C: \(-\frac{1}{2}\csc x\tan x+\frac{1}{2}\ln \left| \sec x-\cot x \right|+C\) D: \(-\frac{1}{2}\sec x\tan x-\frac{1}{2}\ln \left| \csc x+\tan x \right|+C\)