急设x=2t^(2)-1,y=根号(1+t^2).求dy/dx和d^2y/dx^2
举一反三
- 设x=1+t^2、y=cost求dy/dx和d^2y/dx^2sint-tcost/4t^3和sint-tcost/4t^2哪个对?
- 下列方程中，不是全微分方程的为（ ）。 A: \(\left( {3{x^2} + 6x{y^2}} \right)dx + \left( {6{x^2}y + 4{y^2}} \right)dy = 0\) B: \({e^y}dx + \left( {x \cdot {e^y} - 2y} \right)dy = 0\) C: \(y\left( {x - 2y} \right)dx - {x^2}dy = 0\) D: \(\left( { { x^2} - y} \right)dx - xdy = 0\)
- 求方程$y\frac{{{d}^{2}}y}{d{{x}^{2}}}-(\frac{dy}{dx})^{2}=0$的通解： A: $y={{C}_{1}}{{e}^{-{{C}_{2}}x}}$ B: $y={{C}_{1}}{{e}^{-{{C}_{2}}{{x}^{2}}}}$ C: $y={{C}_{1}}x{{e}^{-{{C}_{2}}{{x}^{2}}}}$ D: $y={{C}_{1}}{{e}^{{{C}_{2}}x}}$
- 函数\(z = {e^ { { x^2} - 2y}}\)的全微分为 A: \(<br/>dz = 2x{e^ { { x^2} - 2y}}dx +2{e^ { { x^2} - 2y}}dy\) B: \(<br/>dz = 2x{e^ { { x^2} - 2y}}dx - 2{e^ { { x^2} - 2y}}dy\) C: \(<br/>dz = 2x{e^ { { x^2} - 2y}}dy+ 2{e^ { { x^2} - 2y}}dx\) D: \(<br/>dz = 2x{e^ { { x^2} - 2y}}dy - 2{e^ { { x^2} - 2y}}dx\)
- \( \int_0^1 {dx} \int_ { { x^2}}^x { { {\left( { { x^2} + {y^2}} \right)}^{ - {1 \over 2}}}dy} \) =（ ） A: \( \sqrt 2 + 1 \) B: \( \sqrt 2 - 1 \) C: \( \sqrt 2 \) D: \( \pi \)