Question

求下列方程所确定的隐函数的导数dy/dx

1。y=cosx+1/2siny 2.。 x^2y-e^(2x)=siny 3。xy=e^(x+y)

Answer 1

1. y=cosx+1/(2siny)

   y'=-sinx-0.5cosy y'/sin^2y

   y'(1+0.5cosy/sin^2y)=-sinx

   y' = -sinx/(2+0.5cosy/sin^2y)

2. x^2 y-e^(2x)=siny

   2xy+x^2 y'=cosy y' +2e^(2x)     y'[x^2-cosy]=2e^(2x)-2xy    y'=2[e^(2x)-xy]/(x^2-cosy)

3. xy=e^(x+y)    y+xy'=e^(x+y) (1+y')   y'[1-e^(x+y)]=[e^(x+y)-y]    y'=[e^(x+y)-y]/[1-e^(x+y)]