设f(x)=(1+1/x)x,则f′(1/2)=()
A: -2/3
B: 3(ln3-ln2)
C: 3(ln3-ln2-2/3)
D: 3(ln3-2/3)
A: -2/3
B: 3(ln3-ln2)
C: 3(ln3-ln2-2/3)
D: 3(ln3-2/3)
举一反三
- 由\( y = {1 \over x},\;y = x,\;x = 2 \)围成的平面图形面积为( )。 A: \( {3 \over 2} \) B: \( \ln 2 \) C: \( {3 \over 2} - \ln 2 \) D: \( {3 \over 2} + \ln 2 \)
- 已知\( y = \cos (2 + \ln 3) \),则\( y' \)为( ). A: 0 B: \( \cos (2 + \ln 3) \) C: \( - \sin (2 + \ln 3) \) D: \( - {1 \over 3}\sin (2 + \ln 3) \)
- Calculate the integral:$\int_2^{+\infty}\frac{dx}{x^2-1}$Which answer is CORRECT? A: $\frac12\ln 3$ B: $\ln 3$ C: $\frac{1}{2}$ D: $\frac{1}{2}\ln x$
- 函数$y={{\ln }^{3}}{{x}^{2}}$的微分为( )。 A: $\text{d}y=6x{{\ln }^{2}}{{x}^{2}}\ \text{d}x$ B: $\text{d}y=\frac{6}{x}{{\ln }^{2}}{{x}^{2}}\ \text{d}x$ C: $\text{d}y=3{{\ln }^{2}}{{x}^{2}}\ \text{d}x$ D: $\text{d}y=2x{{\ln }^{3}}{{x}^{2}}\ \text{d}x$
- 已知\( y = 2{x^3} + 7x + \ln 3 \),则\( {y^{(3)}} \)为 。______