设y=ln(1+x²)，求dy．
举一反三
- 已知y=ln(1+x^2),在x=1处的微分dy=
- 设函数f(x，y)连续，则∫12dx∫x2f(x,y)dy+∫12dy∫y4-yf(x,y)dx=( ). A: ∫12dx∫14-xf(x,y)dy． B: ∫12dx∫x4-xf(x,y)dy C: ∫12dx∫14-yf(x,y)dy． D: ∫12dx∫yyf(x,y)dy
- 设\(z = {\log _y}x\)，求\({z_x}\)= A: \({1 \over {y\ln x}}\) B: \({1 \over {\ln x}}\) C: \({1 \over {x\ln y}}\) D: \({1 \over {ln y}}\)
- 设f（x）=ln（1+x），求f（n）（x）.
- 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: \(dz = y{x^{y - 1}}dy + {x^y}dx\)