微積分 dy/dx求解?

1.
dy / dx
= 2 * ln x * ( ln x )'
= 2 * ln x * (1/x)
= 2 ( ln x ) / x ..... Ans

2.
令 F(x,y) = y + ( ln xy ) - 1 = y -1 + ln x + ln y
Fx = ∂F/∂x = 1/x
Fy = ∂F/∂y = 1 + 1/y = (y+1)/y

dy / dx
= - Fx / Fy
= - 1/x / [ (y+1)/y ]
= - y / [ x(y+1) ] ..... Ans

1.
y=(ln x)^2
dy/dx=2(In x)(1/x)
dydx=(2Inx)/x

2.
y+(In x)+(In y)=1
dy/dx +(1/x)+(1/y)(dy/dx)=0
dy/dx(1-1/y)=-1/x
dy/dx=-y/[x(y-1)]