1、对y=10x^3+18x+arcsin3/x求一阶导数，有：
dy/dx=10*3x^2+18+(3/x)'/√[1-(3/x)^2]
=10*3x^2+18+(-3/x^2)/√[1-(3/x)^2]
=30x^2+18-3/[x√(x^2-9)]。
2、※.二阶导数计算
对dy/dx=30x^2+18-3/[x√(x^2-9)]
继续对x求导有：
dy^2/dx^2
=30*2x+3*[√(x^2-9)+x*2x]/[x^2(x^2-9)]
=60x+3*[√(x^2-9)+2x^2]/[x^2(x^2-9)]
3、※.三阶导数计算
∵dy^2/dx=60x+3*[√(x^2-9)+2x^2]/[x^2(x^2-9)]，
∴dy^3/dx^3
=60x+3*{[x/√(x^2-9)+4x][x^2(x^2-9)]-[√(x^2-9)+2x^2](4x^3-2*9x)}/[x^4(x^2-9)^2]
=60x+3*{[1/√(x^2-9)+4][x^2(x^2-9)]-2[√(x^2-9)+2x^2](2x^2-9)}/[x^3(x^2-9)^2]
=60x+3*{[1+4√(x^2-9)][x^2(x^2-9)]-2[(x^2-9)+2x^2*√(x^2-9)](2x^2-9)}/[x^3*√(x^2-9)^5]
4、=60x+3*[(x^2-9)(2*9-3x^2)-4x^2*√(x^2-9)]/[x^3*√(x^2-9)^5]
=60x+3*[(2*9-3x^2)*(x^2-9)-4x^4*√(x^2-9)]/[x^3*√(x^2-9)^5]
=60x+3*[(2*9-3x^2)*√(x^2-9)-4x^4]/[x^3*(x^2-9)^2]
