y=ln(3x), 则 dy = ( )
A: 1/(3x) dx
B: ln3 dx
C: 1/x dx
D: ln3/x dx
A: 1/(3x) dx
B: ln3 dx
C: 1/x dx
D: ln3/x dx
举一反三
- 求函数$y=x\ln x-x$的微分 A: $(\frac{1}{x}-1)dx$ B: $(\ln x-1)dx$ C: $\ln x$ D: $\ln x dx$
- 函数 $y=\ln \sqrt{x}$的微分为 A: $\frac{1}{2}\ln x dx $ B: $\frac{1}{2}dx$ C: $\frac{1}{2x}dx$ D: $\ln x dx$
- 函数\(z = {x^y}\)的全微分为 A: \(dz = y{x^{y - 1}}dy + {x^y}\ln xdx\) B: \(dz = y{x^{y - 1}}dx + {x^y}dy\) C: \(dz = y{x^{y - 1}}dx + {x^y}\ln xdy\) D: \(dz = y{x^{y - 1}}dy + {x^y}dx\)
- 已知\( y = \ln (x + 1) \)，则\( \frac{dy}{dx}\left| {_{x = 0}} \right. \)=______ 。
- 函数\(z = \ln \left( {3x + {y^4}} \right)\)的全微分为 A: \(dz = { { 3 + {y^4}} \over {3x + {y^4}}}dx + { { 3x + 4{y^3}} \over {3x + {y^4}}}dy\) B: \(dz = {3 \over {3x + {y^4}}}dx + { { 4{y^3}} \over {3x + {y^4}}}dy\) C: \(dz = {3 \over {3x + {y^4}}}dy + { { 4{y^3}} \over {3x + {y^4}}}dx\) D: \(dz = {3 \over {3x + {y^4}}}dx - { { 4{y^3}} \over {3x + {y^4}}}dy\)