A: \( {1 \over {\left| x \right|}} \)
B: \( {1 \over x} \)
C: \( - {1 \over x} \)
D: \( x \)
举一反三
- 函数\(y = 1{\rm{ + }}{1 \over x}\)的导数为（ ）. A: \({\rm{ - }}{1 \over { { x^2}}}\) B: \({1 \over { { x^2}}}\) C: \(\ln \left| x \right|\) D: \( - \ln \left| x \right|\)
- 函数$y = \ln x$，则${\left( {\ln x} \right)^{\left( n \right)}} = {\left( { - 1} \right)^{n - 1}}{{\left( {n - 1} \right)!} \over {{x^n}}}$。（ ）
- 函数\(z = {\left( {xy} \right)^x}\)的全微分为 A: \(dz = \left( { { {\left( {xy} \right)}^x} + \ln xy} \right)dx + x{\left( {xy} \right)^x}dy\) B: \(dz = \left( { { {\left( {xy} \right)}^x} + \ln xy} \right)dx + { { x { { \left( {xy} \right)}^x}} \over y}dy\) C: \(dz = {\left( {xy} \right)^x}\ln xydx + { { x { { \left( {xy} \right)}^x}} \over y}dy\) D: \(dz = {\left( {xy} \right)^x}\left( {1 + \ln xy} \right)dx + { { x { { \left( {xy} \right)}^x}} \over y}dy\)
- $\int {{1 \over {3 + 5\cos x}}} dx = \left( {} \right)$ 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: $\ln \left| {{{\cos x + \sin x} \over {\cos x - \sin x}}} \right| + C$
- 函数\(y = \ln \left( {1 + {x^2}} \right)\)的导数为( ). A: \( { { 2x} \over {1 + {x^2}}}\) B: \( - { { 2x} \over {1 + {x^2}}}\) C: \( { { 2x} \over {1 - {x^2}}}\) D: \( - { { 2x} \over {1 - {x^2}}}\)
内容
- 0
\( \int {({1 \over x} - {2 \over {\sqrt {1 - {x^2}} }})dx} = \)( ) A: \( \ln \left| x \right| + 2\arcsin x + C \) B: \( \ln \left| x \right| - 2\arcsin x + C \) C: \(- \ln \left| x \right| - 2\arcsin x + C \) D: \(- \ln \left| x \right| +2\arcsin x + C \)
- 1
\( {1 \over {1 + x}} \)的麦克劳林公式为（ ）。 A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \) D: \( {1 \over {1 + x}} = 1 - x - { { {x^2}} \over 2}- \cdots - { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \)
- 2
\( \sin x \)的麦克劳林公式为（ ）. A: \( \sin x = x - { { {x^3}} \over {3!}} + { { {x^5}} \over {5!}} - \cdots + {( - 1)^n} { { {x^{2n + 1}}} \over {\left( {2n + 1} \right)!}} + o\left( { { x^{2n + 2}}} \right) \) B: \( \sin x = 1 - { { {x^2}} \over {2!}} + { { {x^4}} \over {4!}} - { { {x^6}} \over {6!}} + \cdots + {( - 1)^n} { { {x^{2n}}} \over {\left( {2n} \right)!}} + o\left( { { x^{2n + 1}}} \right) \) C: \( \sin x = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \)
- 3
已知\( y = {x^{\cos x}} \) ,则\( y' = \left( { - \sin x\ln x + { { \cos x} \over x}} \right){x^{\cos x}} \)( ).
- 4
\( {1 \over {1 + x}} \)的麦克劳林公式为（ ）. A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \)