已知\( y = \ln (\sin x) \)，则\( y' \)为（ ）.
A: \( {1 \over {\sin x}} \)
B: \( {1 \over {\cos x}} \)
C: \( \cot x \)
D: \( - \cot x \)
A: \( {1 \over {\sin x}} \)
B: \( {1 \over {\cos x}} \)
C: \( \cot x \)
D: \( - \cot x \)
举一反三
- 已知\( y = \ln (\cos x) \),则 \( y' \)为（ ）. A: \( - \tan x \) B: \( \tan x \) C: \( {1 \over {\cos x}} \) D: \( \cot x \)
- 已知 \( y = \sin x + \ln 2 \)，则 \( y' = \cos x + {1 \over 2} \)（ ）.
- $\int {{{x\cos x} \over {{{\sin }^3}x}}} dx = \left( {} \right)$ 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)
- 已知\( y = {x^{\cos x}} \) ,则\( y' = \left( { - \sin x\ln x + { { \cos x} \over x}} \right){x^{\cos x}} \)( ).