dⅹ²/dⅹ=2ⅹ

dy²/dⅹ，令μ=y²→

dμ/dx=(dμ/dy)(dy/dⅹ)=2y(dy/dⅹ)

ⅹ² y²=4→

dⅹ²/dⅹ dy²/dⅹ=d4/dⅹ→

2ⅹ 2ydy/dⅹ=0→

dy/dⅹ=-ⅹ/y

点A(1,√3)是圆上的一点，那么这个点的斜率是dy/dⅹ=-ⅹ/y=- 1/ √3→

点正切为(y-√3)/(ⅹ-1)=-1/√3, →y=-(√3/3)x 4√3/ 3

2y siny=(x²/π) 1→

d(2y)/dⅹ d(siny)/dⅹ=

d(ⅹ²/π )/ dⅹ d(1)/dⅹ→

2dy/dⅹ cozydy/dⅹ=2ⅹ/π→

d(2dy/dⅹ)/dⅹ

d(cozydy/dⅹ)/dⅹ=d(2ⅹ/π)/dⅹ

→2d²y/dⅹ² ds/dⅹ=2/π①

s=cozydy/dⅹ

令 u=cosy，m=dy/dⅹ→s=um

ds/dⅹ=mdu/dⅹ udm/dⅹ=

(dy/dⅹ)(du /dⅹ ) cosyd²y/dⅹ²

du/dⅹ=dcosy/dⅹ=

(dcosy/dy)(dy/dx)=-sinydy/dⅹ→

ds /dⅹ=

-siny(dy/dⅹ)² cosy d²y/dⅹ²→① is

d²y/dⅹ²(2 cozy) -siny(dy/dⅹ)²=

π/2(d²y/dⅹ²不同于(dy/dⅹ)²)