✔ 最佳答案
1.u=1/x^2 => u'=-2/x^3y=(u^2+4)^4y'=(dy/du)u'=4(u^2+4)^3*2u(-2/x^3)=-16u(u^2+4)^3/x^3=-16(u^2/x+4/x)^3=-16(1/x^3+4/x)^3=-16(1+4x^2)^3/x
2.yx^2+2xy^3-x=3y'x^2+2xy+2y^3+6xy'y^2-1=0y'(x^2+6xy^2)=1-2xy-2y^3y'=(1-2xy-2y^3)/x(x+6y^2)
3.x^2(1-y')+2x(x-y)=1+y'x^2+2x(x-y)-1=(1+x^2)y'y'=(3x^2-2xy-1)/(1+x^2)
4.√x+1=y√y+y1/2√x=1.5√y*y'+y'y'=1/2√x(1.5√y+1)=1/√x(3√y+2)
5.y=2x*sinx + cosxy'=2sinx + 2xcosx - sinx= sinx + 2x*cosx
6.y=(cos2x)^2y'=2cos2x*(-sin2x)*2=-4cos2x*sin2x=-2sin4x
7.y=asin(1/x)y'=1/√(1-1/x^2)*(1/x)'=-1/x^2/[√(x^2-1)/x]=-1/x√(x^2-1)