求函数y=10x^3+18x+arcsin3.x的导数

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]